Question

Solve the quadratic expression by completing the square.
x^2 + 10x – 17 = 7

Answer 1

Problem there is no y...so no need to complete square. You should factor it
first subtract the 7
then it factors into (x+12)(x-2)
So the roots are -12 and 2

Answer 2

1) make the coeffi. of x^2 as 1.
2) Add square of half of the coeffi. of x on both sides.\[x^2 +10x-17=7\]
\[x^2 +10x-17 + (\frac{10}{2})^2=7+(\frac{10}{2})^2\]
\[x^2 +10x-17 + 25=7+25\]
\[x^2 +10x+ 25 -17=32\]
\[x^2 +10x+ 25=49\]
\[(x+5)^2=49\]
\[(x+5)=\pm7\]

taking +7
\[(x+5)=7\] \[x=7-5\]


taking -7
\[x+5=-7\]
\[x=-7-5\]


so roots: 2,-12

Answer 3

x^2 + 10x - 17 = 7
Add 17 to both sides
x^2 + 10x = 24
To complete the square on the left sides, you need a third term. That term is just a number and it is calculated by taking the middle coefficient, 10, dividing it by 2, and then squaring it. Once you add it to the left side, you must add the same number to the right side. 10/2 = 5; 5^2 = 25
x^2 + 10x + 25 = 24 + 25
x^2 + 10x + 25 = 49
(x + 5)^2 = 49
x + 5 = 7 or x + 5 = -7
x = 2 or x = -12

Answer 4

thank you so much mathstudent55, you are a big help

Answer 5

You're welcome