Question

Solve for x in the equation x^2-14x+31=63.

Answer 1

x = 16 or x = -2

Explanation:

Points to remember

Solution of a quadratic equation ax² + bx + = 0 is given by

x = [-b ± √(b² - 4ac) ]/2a

To find the solution of equation

We have x² - 14x + 31 = 63

x² - 14x + 31 - 63 = 0

x² - 14x - 32 = 0

a = 1, b = -14 and c = 32

x = [-b ± √(b² - 4ac) ]/2a

= x = [- -14 ± √((-14)² - 4*1 * (-32)) ]/2*1

= [14 ± √324]/2

x = -2 or x = 16

Answer 2

-2; 16

Explanation:

Rewrite the equation
`x^2-14x+31=63` as:

`x^2-14x+31-63=0\\ \\x^2-14x-32=0`

Now use the quadratic formula:

`D=b^2-4ac\\ \\D=(-14)^2-4\cdot 1\cdot (-32)\ \ [a=1,\ b=-14,\ c=-32]\\ \\D=196+128=324=18^2`

Now

`x_(1,2)=(-b\pm√(D))/(2a)\\ \\x_(1,2)=(-(-14)\pm√(18^2))/(2\cdot 1)=(14\pm18)/(2)=(-4)/(2),\ (32)/(2)=-2,\ 16`