-x^2+7x=8

Simple and best practice solution for -x^2+7x=8 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+7x=8 equation:


Simplifying
-1x2 + 7x = 8

Reorder the terms:
7x + -1x2 = 8

Solving
7x + -1x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 7x + -1x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
8 + -7x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -7x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x + x2 = 0 + -8
-7x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7x + x2 = -8

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -8 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7x + x2 = 4.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + -3.5 = 2.061552813 Simplifying x + -3.5 = 2.061552813 Reorder the terms: -3.5 + x = 2.061552813 Solving -3.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.061552813 + 3.5 x = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 x = 5.561552813 Simplifying x = 5.561552813

Subproblem 2

x + -3.5 = -2.061552813 Simplifying x + -3.5 = -2.061552813 Reorder the terms: -3.5 + x = -2.061552813 Solving -3.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.061552813 + 3.5 x = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 x = 1.438447187 Simplifying x = 1.438447187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.561552813, 1.438447187}

See similar equations:

| y=2x^3-8x^2+18x-72 | | 40+d=2d+30 | | t/=12.6 | | 9=2n-21 | | -68=-5y-13 | | y=15x-4 | | 2/8=-3 | | 11=7x-10 | | 5(x+4)=13x-32 | | 5d+4d+3d-8=3d | | 2n-(8+2n)=6(3n-4) | | -14x+-7y=-9 | | 32=6m+14 | | 24x+16y=-25 | | (x+7)*5=((x+25)+7) | | 3y-3+y=1 | | 5(10k+1)+2(2+8k)=66k+9 | | -14x+-7=-9 | | 5x+12=7x-12 | | 2m-5=8 | | 8k-5(-5k+3)=33k-15 | | 2(y+1)-(y-5)=4(y-2)-3(y-5) | | 1x+6=7+.2x | | 3D+5c=145 | | 2x^3=1 | | 8k-5(-5k+3)=33k+15 | | x-60y=-30 | | 8.5=2(3.14)r | | 2(9s+9)-9s=3(3s+6)-21 | | X-6=3x+1 | | (5a+4)(3a+7)= | | 6(7-3y)+6(y+1)=-12y-48 |

Equations solver categories