4x^2=8x+7

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Solution for 4x^2=8x+7 equation:


Simplifying
4x2 = 8x + 7

Reorder the terms:
4x2 = 7 + 8x

Solving
4x2 = 7 + 8x

Solving for variable 'x'.

Reorder the terms:
-7 + -8x + 4x2 = 7 + 8x + -7 + -8x

Reorder the terms:
-7 + -8x + 4x2 = 7 + -7 + 8x + -8x

Combine like terms: 7 + -7 = 0
-7 + -8x + 4x2 = 0 + 8x + -8x
-7 + -8x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-7 + -8x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + -2x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -2x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -2x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -2x + x2 = 0 + 1.75
-2x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-2x + x2 = 1.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.75 + 1

Reorder the terms:
1 + -2x + x2 = 1.75 + 1

Combine like terms: 1.75 + 1 = 2.75
1 + -2x + x2 = 2.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -1) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + -1 = 1.658312395 Simplifying x + -1 = 1.658312395 Reorder the terms: -1 + x = 1.658312395 Solving -1 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.658312395 + 1 x = 1.658312395 + 1 Combine like terms: 1.658312395 + 1 = 2.658312395 x = 2.658312395 Simplifying x = 2.658312395

Subproblem 2

x + -1 = -1.658312395 Simplifying x + -1 = -1.658312395 Reorder the terms: -1 + x = -1.658312395 Solving -1 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.658312395 + 1 x = -1.658312395 + 1 Combine like terms: -1.658312395 + 1 = -0.658312395 x = -0.658312395 Simplifying x = -0.658312395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.658312395, -0.658312395}

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