144=5x^2-8x+11

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Solution for 144=5x^2-8x+11 equation:


Simplifying
144 = 5x2 + -8x + 11

Reorder the terms:
144 = 11 + -8x + 5x2

Solving
144 = 11 + -8x + 5x2

Solving for variable 'x'.

Combine like terms: 144 + -11 = 133
133 + 8x + -5x2 = 11 + -8x + 5x2 + -11 + 8x + -5x2

Reorder the terms:
133 + 8x + -5x2 = 11 + -11 + -8x + 8x + 5x2 + -5x2

Combine like terms: 11 + -11 = 0
133 + 8x + -5x2 = 0 + -8x + 8x + 5x2 + -5x2
133 + 8x + -5x2 = -8x + 8x + 5x2 + -5x2

Combine like terms: -8x + 8x = 0
133 + 8x + -5x2 = 0 + 5x2 + -5x2
133 + 8x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
133 + 8x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-26.6 + -1.6x + x2 = 0

Move the constant term to the right:

Add '26.6' to each side of the equation.
-26.6 + -1.6x + 26.6 + x2 = 0 + 26.6

Reorder the terms:
-26.6 + 26.6 + -1.6x + x2 = 0 + 26.6

Combine like terms: -26.6 + 26.6 = 0.0
0.0 + -1.6x + x2 = 0 + 26.6
-1.6x + x2 = 0 + 26.6

Combine like terms: 0 + 26.6 = 26.6
-1.6x + x2 = 26.6

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 26.6 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 26.6 + 0.64

Combine like terms: 26.6 + 0.64 = 27.24
0.64 + -1.6x + x2 = 27.24

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 27.24

Calculate the square root of the right side: 5.21919534

Break this problem into two subproblems by setting 
(x + -0.8) equal to 5.21919534 and -5.21919534.

Subproblem 1

x + -0.8 = 5.21919534 Simplifying x + -0.8 = 5.21919534 Reorder the terms: -0.8 + x = 5.21919534 Solving -0.8 + x = 5.21919534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 5.21919534 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 5.21919534 + 0.8 x = 5.21919534 + 0.8 Combine like terms: 5.21919534 + 0.8 = 6.01919534 x = 6.01919534 Simplifying x = 6.01919534

Subproblem 2

x + -0.8 = -5.21919534 Simplifying x + -0.8 = -5.21919534 Reorder the terms: -0.8 + x = -5.21919534 Solving -0.8 + x = -5.21919534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -5.21919534 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -5.21919534 + 0.8 x = -5.21919534 + 0.8 Combine like terms: -5.21919534 + 0.8 = -4.41919534 x = -4.41919534 Simplifying x = -4.41919534

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.01919534, -4.41919534}

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