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Simplifying 2x2 + 32x + -18 = 0 Reorder the terms: -18 + 32x + 2x2 = 0 Solving -18 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 16x + x2) = 0 Ignore the factor 2.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 = 0.544003745 x = 0.544003745 Simplifying x = 0.544003745Subproblem 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 = -16.544003745 x = -16.544003745 Simplifying x = -16.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.544003745, -16.544003745}Solution
x = {0.544003745, -16.544003745}
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