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# One of the solutions to x^{2} - 2x - 15 = 0 is x = -3. What is the other solution?

x = -5, x = -1, x = 1, x = 5

**Solution:**

Given that, x^{2} - 2x - 15 = 0

Let us solve this quadratic equation by splitting the middle term.

x^{2} - 5x -3x - 15 = 0

x(x - 5) - 3(x- 5) = 0

(x + 3)(x - 5) = 0

Therefore, the roots are (x + 3) = 0 ⇒ x = -3 and

(x - 5) = 0 ⇒ x = 5

Therefore, the other solution is x = 5.

Aliter

From the options given, substitute the values of x in the given quadratic equation, x^{2} - 2x - 15 = 0.

When x = -5,

L.H.S. = x2 - 2x - 15 = (-5)2 -2(-5) - 15 = 20

L.H.S. ≠ R.H.S.

When x = 5

L.H.S. = x^{2} - 2x - 15 = (5)^{2} -2(5) - 15 = 0

L.H.S. = R.H.S.

Therefore, the other solution is x = 5.

Aliter

Using the synthetic division method,

Remainder = 0

Quotient = x - 5

∴ x - 5 = 0 ⇒ x = 5

∴ The other solution is x = 5.

## One of the solutions to x^{2} - 2x - 15 = 0 is x = -3. What is the other solution?

**Summary:**

If one of the solutions to x^{2} - 2x - 15 = 0 is x = -3, the other solution is x = 5.

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