(2x)(2x)+16x-7=0

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Solution for (2x)(2x)+16x-7=0 equation:


Simplifying
(2x)(2x) + 16x + -7 = 0

Remove parenthesis around (2x)
2x(2x) + 16x + -7 = 0

Remove parenthesis around (2x)
2x * 2x + 16x + -7 = 0

Reorder the terms for easier multiplication:
2 * 2x * x + 16x + -7 = 0

Multiply 2 * 2
4x * x + 16x + -7 = 0

Multiply x * x
4x2 + 16x + -7 = 0

Reorder the terms:
-7 + 16x + 4x2 = 0

Solving
-7 + 16x + 4x2 = 0

Solving for variable 'x'.

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

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

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 4x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 4x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 4x + x2 = 0 + 1.75
4x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
4x + x2 = 1.75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.75 + 4

Reorder the terms:
4 + 4x + x2 = 1.75 + 4

Combine like terms: 1.75 + 4 = 5.75
4 + 4x + x2 = 5.75

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 2) equal to 2.397915762 and -2.397915762.

Subproblem 1

x + 2 = 2.397915762 Simplifying x + 2 = 2.397915762 Reorder the terms: 2 + x = 2.397915762 Solving 2 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.397915762 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.397915762 + -2 x = 2.397915762 + -2 Combine like terms: 2.397915762 + -2 = 0.397915762 x = 0.397915762 Simplifying x = 0.397915762

Subproblem 2

x + 2 = -2.397915762 Simplifying x + 2 = -2.397915762 Reorder the terms: 2 + x = -2.397915762 Solving 2 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.397915762 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.397915762 + -2 x = -2.397915762 + -2 Combine like terms: -2.397915762 + -2 = -4.397915762 x = -4.397915762 Simplifying x = -4.397915762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.397915762, -4.397915762}

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