Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 15, 2023

Find the solutions to the quadratic equation $(2h + 13)^2 - 3 = 0$ . The solutions are $\frac{-13 \pm \sqrt{169}}{2}$ .

STEP 1

Assumptions1. We are looking for all solutions of the equation $(h+13)^ -3 =0$ . . The solutions can be real or complex numbers.

STEP 2

First, we need to isolate the square term on one side of the equation. We can do this by adding to both sides of the equation.
$(2h+13)^2 =$

STEP 3

Next, we take the square root of both sides of the equation. Remember that the square root of a number is both its positive and negative root.
$2h+13 = \pm \sqrt{3}$

STEP 4

Subtract13 from both sides of the equation to isolate $2h$ .
$2h = \pm \sqrt{3} -13$

STEP 5

Finally, divide both sides of the equation by2 to solve for $h$ .
$h = \frac{\pm \sqrt{3} -13}{2}$ The solutions of the equation are $h = \frac{\sqrt{3} -13}{2}$ and $h = \frac{-\sqrt{3} -13}{2}$ .

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