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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

9. Proofs Using Coordinate Geometry

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Exercise 39 Page 418

Consider the positive and negative solutions when isolating a variable raised to the power of two.

5 and - 5

Practice makes perfect

We will solve the given equation by taking the square roots. Remember to consider the positive and negative solutions.

y^2+10 = 35

LHS-10=RHS-10

y^2 = 25

sqrt(LHS)=sqrt(RHS)

sqrt(y^2)=sqrt(25)

sqrt(a^2)=± a

y=±sqrt(25)

Calculate root

y=± 5

We found that y=± 5. Thus, there are two solutions for the equation, which are y= 5 and y= - 5.

Checking Our Answer

Checking our answer

We can check our answers by substituting them for y in the given equation. Let's start with y=- 5.

y^2+10=35

y= - 5

( - 5)^2+10? =35

▼

Simplify

NegBaseToPosPow

(- a)^2 = a^2

5^2+10? =35

Calculate power

25+10? =35

Add terms

35=35 ✓

Since 35=35, we know that y=- 5 is a solution of the equation. Let's check if y=5 is also a solution.

y^2+10=35

y= 5

5^2+10? =35

▼

Simplify

Calculate power

25+10? =35

Add terms

35=35 ✓

Again, since 35=35, we know that y=5 is a solution of the equation.

Subchapter links

Lesson Check p.416

Standardized Test Prep p.418

Mixed Review p.418