Question

Solve each equation. $$ (q-2)^{2}+8=44 $$

   Solve each equation. 
$$
(q-2)^{2}+8=44
$$

Impact Mathematics Algebra and More

Impact Mathematics Algebra and More

McGraw Hill 1st Edition

Chapter 7, Problem 12

Instant Answer

Solved by Expert Sriram Soundarrajan

07/03/2020

Step 1

We can do this by subtracting 8 from both sides of the equation: $$ (q-2)^{2}+8-8=44-8 $$ This simplifies to: $$ (q-2)^{2}=36 $$ Show more…

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Solve each equation. $$ (q-2)^{2}+8=44 $$

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Key Concepts

Solving Quadratic Equations

This overall approach involves methods for solving equations where a variable is raised to the second power. Techniques such as isolating the squared term, taking square roots, and checking for extraneous solutions are fundamental methods in handling quadratic equations.

Isolating the Squared Term

This concept involves rearranging an equation so that the term containing the variable squared is by itself on one side of the equation. This step is vital because it simplifies the equation and sets the stage for applying inverse operations to solve for the variable.

Taking Square Roots

After isolating the squared expression, the next step is to apply the square root to both sides of the equation. It is important to consider both the positive and negative square roots, as squaring either a positive or negative number yields the same result.

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