Solving the 'Impossible' Equation | JAMB & WAEC Mathematics 2026 Revision"

Ajouté : 2026-05-10

[00:00:01]This is complex exponential equation.

[00:00:05]And we want to find the value of x.

[00:00:08]So, by the end of this video, you will know the solution to this complex exponential equation.

[00:00:13]So, follow me step by step as I solve this together.

[00:00:17]We have the square root of 2 to the power of the root of x is equal to 2 to the power of x + 2.

[00:00:23]Let me show you how to solve this.

[00:00:25]This is very simple. Watch.

[00:00:28]Now, I am looking for a way to clear this square root in the left-hand side.

[00:00:34]Now, to clear this square root, you need to square both side to clear this square root.

[00:00:39]So, squaring both side, we shall have you square this side and also what?

[00:00:43]Square this side.

[00:00:46]Which means this will cancel out this.

[00:00:49]So, you are left with 2 to the power of the root of x 2 to the power of the root of x will be equal to Now, look at here. This squared means I should write this in two places.

[00:01:01]Which means we shall have 2 to the power of x + 2 all multiplied by 2 to the power of x + 2.

[00:01:12]Which means when we have the same base, what do you do? You add the powers by picking one of the base one of the property of indices.

[00:01:21]So, if we pick one of the base, we shall add the exponent because we are multiplying this.

[00:01:28]Okay? So, this become 2 to the power of the root of x will be equal to just add like terms.

[00:01:36]x + x is 2x. Pick one of this, which is 2 to the power of 2x. Okay? Because x + x is 2x. You put the plus sign. Plus 2 + 2 is what?

[00:01:48]Is um four.

[00:01:51]This is what you shall have.

[00:01:53]So, observe that the base are expressed the same. What are you going to do? You're going to equate the powers. Okay? So, equating the powers, we shall have the root of x will be equal to 2x + 4.

[00:02:11]Now, look at this. We still need to square both side because of the square root.

[00:02:17]Squaring both side will make this equation to become a quadratic equation.

[00:02:21]Why which we are going to apply a quadratic formula to solve.

[00:02:26]Because I believe if we square both side, this will result to a quadratic equation.

[00:02:30]That quadratic equation cannot be factorized.

[00:02:32]So, let's square both side and see what we shall have. So, if you square both side, you square this side and you also what? You square this side.

[00:02:40]This neutralize this.

[00:02:42]This means you should rewrite this in two places.

[00:02:45]Which means we shall have x to be equal to 2x + 4 multiplied by 2x + 4.

[00:02:57]Now, we shall have x to be equal to 2x * 2x is 4x squared. Okay? 2x * 4 will what? Plus 8x. You put a plus sign.

[00:03:11]4 * 2x will become 8x plus 4 * 4 is 16.

[00:03:18]Which we have a quadratic equation.

[00:03:21]So, we shall have x if this add this we shall have 16, right?

[00:03:27]But this is like thing with this because of space. Let me just do some cancellation of 8. So, this is 8x + 8x.

[00:03:36]If you add this because they are like terms, we shall have 16.

[00:03:41]And this 16 minus 16x minus x will become 15x. So, permit me to write this equation as 4x squared okay? Plus 15 x plus what? 16 will be equal to zero.

[00:04:00]Right?

[00:04:02]So, let us apply a quadratic formula to solve this.

[00:04:06]So, the quadratic formula said that x will be equal to -b plus or minus square root of b squared -4 ac all divided by 2 a.

[00:04:22]Now, let us plug in um this to this quadratic formula and see what we shall have.

[00:04:29]>> [snorts] >> So, this is our a, this is our b, and this is our c.

[00:04:34]So, our x will be equal to I hope you are seeing it clearly.

[00:04:38]Our x shall be equal to -b Our b is 15, which is -15.

[00:04:43]Plus or minus the square root of b squared is 15 squared. And 15 squared is 225 minus um 4 a Our a is 4, so 4 * 4 * c Our c is 16. 4 * 4 16 16 * 16 is 256. So, this is 256. 56. All this is divided by 2 * Our a is 4, so 2 * 4 is um 8. So, this is 8, okay?

[00:05:21]So, this is what we shall have. I hope you are following me up to this point.

[00:05:24]It is very simple to solve.

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[00:05:31]Okay. Now, if you subtract 225 minus 200 200 and 56, this will give us a complex thing or a complex solution.

[00:05:41]So, we shall have our x to be equal to 15 plus or minus If subtract this we shall have the square root of minus 31 all divided by 8.

[00:05:57]Okay?

[00:05:58]So now Do you know that the square root of minus 31 is the same thing as saying the square root of minus one?

[00:06:07]Are you seeing clearly times the square root of 31? Of course the square root of minus one is a complex.

[00:06:15]So that means the square root of minus 31 31 is equal to I root of what 31.

[00:06:25]So this become our X to be equal to minus 15 plus or minus I root of 31 divided by 8.

[00:06:38]So now I'm going to get two solutions because of this plus and minus.

[00:06:44]Right? So our first solution is for minus which means we shall have our X to be equal to minus 15 minus I root of 31 divided by 8. That's for X1 X1. So our X2 will be equal to minus 15 plus I root of 31 divided by 8. So these are the two solutions to this amazing complex exponential equation. I hope you enjoyed this video. Help us to share this video, follow us and subscribe to our channel for more math tips like this. Thank you.