/*! 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 82 Explain how to solve \((x-1)^{2}... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 82

Explain how to solve \((x-1)^{2}=16\) using the square root property.

Short Answer

Expert verified
The solutions to the equation \((x-1)^{2}=16\) are \(x=5\) and \(x=-3\).

Step by step solution

01

Isolate the squared term

In the given equation the squared term is already isolated, i.e., \((x-1)^{2}=16\).
02

Square Root Property

Now,apply the square root property by taking the square root of both sides. This gives us \(x-1 = \sqrt{16}\) and \(x-1 = -\sqrt{16}\). Remember, when we take the square root of both sides we need to consider both positive and negative roots.
03

Simplify Square Roots

Now simplify the square root of 16. The square root of 16 is 4. So, the equations become \(x-1=4\) and \(x-1=-4\).
04

Solve for x

To isolate x, add 1 to both sides in each equation. This gives two solutions: \(x=4+1=5\) and \(x=-4+1=-3\).

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