Question

Solve each equation. $$ 2(x-4)^{2}+5=7 $$

   Solve each equation. 
$$
2(x-4)^{2}+5=7
$$

Impact Mathematics Algebra and More

Impact Mathematics Algebra and More

McGraw Hill 1st Edition

Chapter 7, Problem 8

Instant Answer

Solved by Expert Sriram Soundarrajan

07/03/2020

Step 1

This gives us: $$ 2(x-4)^{2}+5-5=7-5 $$ which simplifies to: $$ 2(x-4)^{2}=2 $$ Show more…

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Solve each equation. $$ 2(x-4)^{2}+5=7 $$

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Key Concepts

Isolating the Squared Expression

This involves rearranging the equation so that the squared term stands alone on one side. In equations where a variable expression is squared and combined with other terms, inverse operations such as subtraction and division are used to isolate the squared term before any further steps are taken.

Square Root Property

Once the squared expression is isolated, the square root property is applied to 'undo' the squaring. This process involves taking the square root of both sides of the equation while remembering to consider both the positive and negative roots, as both can yield valid solutions for the original equation.

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