-4x^2+6x+5=x

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Solution for -4x^2+6x+5=x equation:


Simplifying
-4x2 + 6x + 5 = x

Reorder the terms:
5 + 6x + -4x2 = x

Solving
5 + 6x + -4x2 = x

Solving for variable 'x'.

Reorder the terms:
5 + 6x + -1x + -4x2 = x + -1x

Combine like terms: 6x + -1x = 5x
5 + 5x + -4x2 = x + -1x

Combine like terms: x + -1x = 0
5 + 5x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -1.25x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.25x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.25x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.25x + x2 = 0 + 1.25
-1.25x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.25x + x2 = 1.25

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 1.25 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 1.25 + 0.390625

Combine like terms: 1.25 + 0.390625 = 1.640625
0.390625 + -1.25x + x2 = 1.640625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.280868846 and -1.280868846.

Subproblem 1

x + -0.625 = 1.280868846 Simplifying x + -0.625 = 1.280868846 Reorder the terms: -0.625 + x = 1.280868846 Solving -0.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.280868846 + 0.625 x = 1.280868846 + 0.625 Combine like terms: 1.280868846 + 0.625 = 1.905868846 x = 1.905868846 Simplifying x = 1.905868846

Subproblem 2

x + -0.625 = -1.280868846 Simplifying x + -0.625 = -1.280868846 Reorder the terms: -0.625 + x = -1.280868846 Solving -0.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.280868846 + 0.625 x = -1.280868846 + 0.625 Combine like terms: -1.280868846 + 0.625 = -0.655868846 x = -0.655868846 Simplifying x = -0.655868846

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.905868846, -0.655868846}

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