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To solve the given equation by factoring.
![Check Mark](/static/check-mark.png)
Answer to Problem 32SGR
The value of g is -15 and -1 .
Explanation of Solution
Given information :
The equation provided is (g+8)2=49 .
Formula used :
The given equation can be solved by factoring. To do so, break up the midpoint to arrive at two factors. Then use the zero-product property to equate each factor in order to get the roots.
Calculation :
(g+8)2=49
Given equation.
=>g2+16g+64−49=0
On expanding and subtracting 49 from both sides.
=>g2+16g+15=0
Equation to be solved.
=>g2+15g+g+15=0
Breaking the middle term that when multiplied, provides that values of ax2×c .
=>g(g+15)+1(g+15)=0
Arranging the common factors.
=>(g+1)(g+15)=0
The two factors of the function.
Now, the first root is:
g+1=0
Using zero-product property.
g=−1
The second root is:
g+15=0
Using zero-product property.
g=−15
Thus, the values of g are -15 and -1 .
To check the solutions, put them in the given equation and verify that left-hand and right-hand sides are equal.
For g=−1
Putting the value in the equation.
(−1)2+16(−1)+15=0
Simplifying the expression.
=>1−16+15=0
Hence this result is a success.
Now, for g=−15
(−15)2+16(−15)+15=0
Putting the value in the equation.
=>225−240+15=0
Simplifying the expression.
=>240−240=0
Hence this result is a success.
Chapter 9 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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