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Simplifying 2x2 + -20x + -64 = 0 Reorder the terms: -64 + -20x + 2x2 = 0 Solving -64 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -10x + x2)' equal to zero and attempt to solve: Simplifying -32 + -10x + x2 = 0 Solving -32 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -10x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -10x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -10x + x2 = 0 + 32 -10x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -10x + x2 = 32 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 = 32 + 25 Reorder the terms: 25 + -10x + x2 = 32 + 25 Combine like terms: 32 + 25 = 57 25 + -10x + x2 = 57 Factor a perfect square on the left side: (x + -5)(x + -5) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -5) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -5 = 7.549834435 Simplifying x + -5 = 7.549834435 Reorder the terms: -5 + x = 7.549834435 Solving -5 + x = 7.549834435 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 = 7.549834435 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.549834435 + 5 x = 7.549834435 + 5 Combine like terms: 7.549834435 + 5 = 12.549834435 x = 12.549834435 Simplifying x = 12.549834435Subproblem 2
x + -5 = -7.549834435 Simplifying x + -5 = -7.549834435 Reorder the terms: -5 + x = -7.549834435 Solving -5 + x = -7.549834435 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 = -7.549834435 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.549834435 + 5 x = -7.549834435 + 5 Combine like terms: -7.549834435 + 5 = -2.549834435 x = -2.549834435 Simplifying x = -2.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.549834435, -2.549834435}Solution
x = {12.549834435, -2.549834435}
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