5x^2=8x+6

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Solution for 5x^2=8x+6 equation:


Simplifying
5x2 = 8x + 6

Reorder the terms:
5x2 = 6 + 8x

Solving
5x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
-6 + -8x + 5x2 = 6 + 8x + -6 + -8x

Reorder the terms:
-6 + -8x + 5x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
-6 + -8x + 5x2 = 0 + 8x + -8x
-6 + -8x + 5x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-6 + -8x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -1.6x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -1.6x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -1.6x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -1.6x + x2 = 0 + 1.2
-1.6x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-1.6x + x2 = 1.2

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 = 1.2 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 1.2 + 0.64

Combine like terms: 1.2 + 0.64 = 1.84
0.64 + -1.6x + x2 = 1.84

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.356465997 and -1.356465997.

Subproblem 1

x + -0.8 = 1.356465997 Simplifying x + -0.8 = 1.356465997 Reorder the terms: -0.8 + x = 1.356465997 Solving -0.8 + x = 1.356465997 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 = 1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.356465997 + 0.8 x = 1.356465997 + 0.8 Combine like terms: 1.356465997 + 0.8 = 2.156465997 x = 2.156465997 Simplifying x = 2.156465997

Subproblem 2

x + -0.8 = -1.356465997 Simplifying x + -0.8 = -1.356465997 Reorder the terms: -0.8 + x = -1.356465997 Solving -0.8 + x = -1.356465997 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 = -1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.356465997 + 0.8 x = -1.356465997 + 0.8 Combine like terms: -1.356465997 + 0.8 = -0.556465997 x = -0.556465997 Simplifying x = -0.556465997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.156465997, -0.556465997}

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