x^2=4(5x+7)

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Solution for x^2=4(5x+7) equation:


Simplifying
x2 = 4(5x + 7)

Reorder the terms:
x2 = 4(7 + 5x)
x2 = (7 * 4 + 5x * 4)
x2 = (28 + 20x)

Solving
x2 = 28 + 20x

Solving for variable 'x'.

Reorder the terms:
-28 + -20x + x2 = 28 + 20x + -28 + -20x

Reorder the terms:
-28 + -20x + x2 = 28 + -28 + 20x + -20x

Combine like terms: 28 + -28 = 0
-28 + -20x + x2 = 0 + 20x + -20x
-28 + -20x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-28 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -20x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -20x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -20x + x2 = 0 + 28
-20x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-20x + x2 = 28

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 28 + 100

Reorder the terms:
100 + -20x + x2 = 28 + 100

Combine like terms: 28 + 100 = 128
100 + -20x + x2 = 128

Factor a perfect square on the left side:
(x + -10)(x + -10) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + -10) equal to 11.313708499 and -11.313708499.

Subproblem 1

x + -10 = 11.313708499 Simplifying x + -10 = 11.313708499 Reorder the terms: -10 + x = 11.313708499 Solving -10 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 11.313708499 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.313708499 + 10 x = 11.313708499 + 10 Combine like terms: 11.313708499 + 10 = 21.313708499 x = 21.313708499 Simplifying x = 21.313708499

Subproblem 2

x + -10 = -11.313708499 Simplifying x + -10 = -11.313708499 Reorder the terms: -10 + x = -11.313708499 Solving -10 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -11.313708499 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.313708499 + 10 x = -11.313708499 + 10 Combine like terms: -11.313708499 + 10 = -1.313708499 x = -1.313708499 Simplifying x = -1.313708499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.313708499, -1.313708499}

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