x^2=8x+31

Simple and best practice solution for x^2=8x+31 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2=8x+31 equation:


Simplifying
x2 = 8x + 31

Reorder the terms:
x2 = 31 + 8x

Solving
x2 = 31 + 8x

Solving for variable 'x'.

Reorder the terms:
-31 + -8x + x2 = 31 + 8x + -31 + -8x

Reorder the terms:
-31 + -8x + x2 = 31 + -31 + 8x + -8x

Combine like terms: 31 + -31 = 0
-31 + -8x + x2 = 0 + 8x + -8x
-31 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-31 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -8x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -8x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -8x + x2 = 0 + 31
-8x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-8x + x2 = 31

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 31 + 16

Reorder the terms:
16 + -8x + x2 = 31 + 16

Combine like terms: 31 + 16 = 47
16 + -8x + x2 = 47

Factor a perfect square on the left side:
(x + -4)(x + -4) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -4) equal to 6.8556546 and -6.8556546.

Subproblem 1

x + -4 = 6.8556546 Simplifying x + -4 = 6.8556546 Reorder the terms: -4 + x = 6.8556546 Solving -4 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.8556546 + 4 x = 6.8556546 + 4 Combine like terms: 6.8556546 + 4 = 10.8556546 x = 10.8556546 Simplifying x = 10.8556546

Subproblem 2

x + -4 = -6.8556546 Simplifying x + -4 = -6.8556546 Reorder the terms: -4 + x = -6.8556546 Solving -4 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.8556546 + 4 x = -6.8556546 + 4 Combine like terms: -6.8556546 + 4 = -2.8556546 x = -2.8556546 Simplifying x = -2.8556546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.8556546, -2.8556546}

See similar equations:

| -8c+5=-35 | | 13+25x=5(5x+4)-7 | | x*2-3x+2=6 | | (-3-x)(-3-x)=0 | | 12x^2+15x+8x+10= | | 2x-2+3x+12=14 | | 3x-27=-15 | | 4(t-2)=2t+4 | | 9y-6y=24 | | (2-x)(-3-x)(-3-x)=0 | | 4(3y-4)=6+7y | | 6x-2-2x=x+5+x | | 4x-6=y | | 8x-4x=10 | | 3+5q=9 | | 3(x+5)=5x+15 | | x^2+5x+42=9x+2 | | 2(2c-1)-4=2c+2 | | 7(5y-2)=6(6y-1) | | 3(x+2)=x+12 | | 98=7w | | (-2)(4v-w)+6((-3)w-3v)= | | 1.1r+1.4=3.2-r | | 85-5x=13x+15 | | -8(t+4)=16 | | x^3+2x^2+7x-6=0 | | 36=u-9 | | 7j-14=3j+11 | | 33-19=2(x-5) | | 8(2t+1)=7(d-2) | | 8x^3-6x^2+20x-15=0 | | 3x+10=4x-8 |

Equations solver categories