x^2-53x+156=0

Simple and best practice solution for x^2-53x+156=0 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^2-53x+156=0 equation:


Simplifying
x2 + -53x + 156 = 0

Reorder the terms:
156 + -53x + x2 = 0

Solving
156 + -53x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-156' to each side of the equation.
156 + -53x + -156 + x2 = 0 + -156

Reorder the terms:
156 + -156 + -53x + x2 = 0 + -156

Combine like terms: 156 + -156 = 0
0 + -53x + x2 = 0 + -156
-53x + x2 = 0 + -156

Combine like terms: 0 + -156 = -156
-53x + x2 = -156

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = -156 + 702.25

Reorder the terms:
702.25 + -53x + x2 = -156 + 702.25

Combine like terms: -156 + 702.25 = 546.25
702.25 + -53x + x2 = 546.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 546.25

Calculate the square root of the right side: 23.371991785

Break this problem into two subproblems by setting 
(x + -26.5) equal to 23.371991785 and -23.371991785.

Subproblem 1

x + -26.5 = 23.371991785 Simplifying x + -26.5 = 23.371991785 Reorder the terms: -26.5 + x = 23.371991785 Solving -26.5 + x = 23.371991785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = 23.371991785 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 23.371991785 + 26.5 x = 23.371991785 + 26.5 Combine like terms: 23.371991785 + 26.5 = 49.871991785 x = 49.871991785 Simplifying x = 49.871991785

Subproblem 2

x + -26.5 = -23.371991785 Simplifying x + -26.5 = -23.371991785 Reorder the terms: -26.5 + x = -23.371991785 Solving -26.5 + x = -23.371991785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = -23.371991785 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -23.371991785 + 26.5 x = -23.371991785 + 26.5 Combine like terms: -23.371991785 + 26.5 = 3.128008215 x = 3.128008215 Simplifying x = 3.128008215

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.871991785, 3.128008215}

See similar equations:

| 9k^2+12k-12=0 | | 4+2(x-3)=2x-1 | | -2x+5+5x=22 | | 2y^2/32x^17 | | 4-3(x+2)=8-10 | | 0=x^2+14x-38 | | 5*x^2+x^3=112 | | 5*x^2=15 | | 2(4h-6)=4(3b-7) | | x-3/2-4x-1/6=2/3 | | 2x^3/16x^15 | | (10^(-15))/(3.9*10^7)= | | 4y+5y+15=5y+7y | | 79-13x+13x=49-14x+x^2+13x | | -19m+14b= | | 3/4x-6=1/12x | | 6x/2-x/1=x/10-28/5 | | 15-30=6x-(x+5) | | -5(2x+1)+19=-2(x+5) | | 0.2(x+40)-0.02(x-50)=19.8 | | 30=s(x+1) | | 181=-(1-13m) | | y=5/7x-20 | | 8f-2f=-16 | | 19x+26=x+8 | | -0.2x^2+0.8x+1=0 | | 15z-13z= | | 15t+38=10t+13 | | N-7+6=12 | | 14x+14=12x | | 1/4a-2/3a=5/6 | | 2(3y+5)=3(5y+13) |

Equations solver categories