/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 62 Solve each quadratic equation by... [FREE SOLUTION] | 91Ó°ÊÓ

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Solve each quadratic equation by the square root property. $$5 x^{2}=45$$

Short Answer

Expert verified
The solutions to the equation \(5x^2 = 45\) are \(x = 3\) and \(x = -3\)

Step by step solution

01

Isolate \(x^{2}\)

We isolate \(x^2\) by dividing the entire equation by 5. This gives us \(x^{2}= 45/5 = 9\).
02

Apply the Square Root Property

Now we will use the square root property, which tells us that x is equal to \(+\sqrt{k}\) and also equal to \(-\sqrt{k}\). We find that \(x = +\sqrt{9}\) or \(x = -\sqrt{9}\) meaning \(x = 3\) or \(x = -3\).
03

Check the Solution

We check the solution by substituting \(x = 3\) or \(x = -3\) into the original equation \(5x^2 = 45\) and see whether both sides are equal. Doing so, we find that both solutions are valid and are indeed -3 and 3.

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