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Simplifying 4x2 + -64x = 36 Reorder the terms: -64x + 4x2 = 36 Solving -64x + 4x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + -64x + 4x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -64x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -16x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -16x + x2)' equal to zero and attempt to solve: Simplifying -9 + -16x + x2 = 0 Solving -9 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -16x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -16x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -16x + x2 = 0 + 9 -16x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -16x + x2 = 9 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 9 + 64 Reorder the terms: 64 + -16x + x2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + -16x + x2 = 73 Factor a perfect square on the left side: (x + -8)(x + -8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -8) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -8 = 8.544003745 Simplifying x + -8 = 8.544003745 Reorder the terms: -8 + x = 8.544003745 Solving -8 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.544003745 + 8 x = 8.544003745 + 8 Combine like terms: 8.544003745 + 8 = 16.544003745 x = 16.544003745 Simplifying x = 16.544003745Subproblem 2
x + -8 = -8.544003745 Simplifying x + -8 = -8.544003745 Reorder the terms: -8 + x = -8.544003745 Solving -8 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.544003745 + 8 x = -8.544003745 + 8 Combine like terms: -8.544003745 + 8 = -0.544003745 x = -0.544003745 Simplifying x = -0.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.544003745, -0.544003745}Solution
x = {16.544003745, -0.544003745}
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