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Simplifying 4x2 + -40x + -40 = 0 Reorder the terms: -40 + -40x + 4x2 = 0 Solving -40 + -40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -10x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -10x + x2)' equal to zero and attempt to solve: Simplifying -10 + -10x + x2 = 0 Solving -10 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -10x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -10x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -10x + x2 = 0 + 10 -10x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -10x + x2 = 10 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 10 + 25 Reorder the terms: 25 + -10x + x2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + -10x + x2 = 35 Factor a perfect square on the left side: (x + -5)(x + -5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -5) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -5 = 5.916079783 Simplifying x + -5 = 5.916079783 Reorder the terms: -5 + x = 5.916079783 Solving -5 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.916079783 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.916079783 + 5 x = 5.916079783 + 5 Combine like terms: 5.916079783 + 5 = 10.916079783 x = 10.916079783 Simplifying x = 10.916079783Subproblem 2
x + -5 = -5.916079783 Simplifying x + -5 = -5.916079783 Reorder the terms: -5 + x = -5.916079783 Solving -5 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.916079783 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.916079783 + 5 x = -5.916079783 + 5 Combine like terms: -5.916079783 + 5 = -0.916079783 x = -0.916079783 Simplifying x = -0.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.916079783, -0.916079783}Solution
x = {10.916079783, -0.916079783}
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