16x^2+80x+80=0

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Solution for 16x^2+80x+80=0 equation:


Simplifying
16x2 + 80x + 80 = 0

Reorder the terms:
80 + 80x + 16x2 = 0

Solving
80 + 80x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(5 + 5x + x2) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(5 + 5x + x2)' equal to zero and attempt to solve: Simplifying 5 + 5x + x2 = 0 Solving 5 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5x + x2 = 0 + -5 5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5x + x2 = -5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + 5x + x2 = 1.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 2.5 = 1.118033989 Simplifying x + 2.5 = 1.118033989 Reorder the terms: 2.5 + x = 1.118033989 Solving 2.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.118033989 + -2.5 x = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 x = -1.381966011 Simplifying x = -1.381966011

Subproblem 2

x + 2.5 = -1.118033989 Simplifying x + 2.5 = -1.118033989 Reorder the terms: 2.5 + x = -1.118033989 Solving 2.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.118033989 + -2.5 x = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 x = -3.618033989 Simplifying x = -3.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.381966011, -3.618033989}

Solution

x = {-1.381966011, -3.618033989}

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