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Simplifying 2x2 + 64x + -1000 = 0 Reorder the terms: -1000 + 64x + 2x2 = 0 Solving -1000 + 64x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 32x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 32x + x2)' equal to zero and attempt to solve: Simplifying -500 + 32x + x2 = 0 Solving -500 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 32x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 32x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 32x + x2 = 0 + 500 32x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 32x + x2 = 500 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 500 + 256 Reorder the terms: 256 + 32x + x2 = 500 + 256 Combine like terms: 500 + 256 = 756 256 + 32x + x2 = 756 Factor a perfect square on the left side: (x + 16)(x + 16) = 756 Calculate the square root of the right side: 27.49545417 Break this problem into two subproblems by setting (x + 16) equal to 27.49545417 and -27.49545417.Subproblem 1
x + 16 = 27.49545417 Simplifying x + 16 = 27.49545417 Reorder the terms: 16 + x = 27.49545417 Solving 16 + x = 27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 27.49545417 + -16 Combine like terms: 16 + -16 = 0 0 + x = 27.49545417 + -16 x = 27.49545417 + -16 Combine like terms: 27.49545417 + -16 = 11.49545417 x = 11.49545417 Simplifying x = 11.49545417Subproblem 2
x + 16 = -27.49545417 Simplifying x + 16 = -27.49545417 Reorder the terms: 16 + x = -27.49545417 Solving 16 + x = -27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -27.49545417 + -16 Combine like terms: 16 + -16 = 0 0 + x = -27.49545417 + -16 x = -27.49545417 + -16 Combine like terms: -27.49545417 + -16 = -43.49545417 x = -43.49545417 Simplifying x = -43.49545417Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.49545417, -43.49545417}Solution
x = {11.49545417, -43.49545417}
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