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Simplifying 2x2 + -32x = 10 Reorder the terms: -32x + 2x2 = 10 Solving -32x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -32x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -16x + x2)' equal to zero and attempt to solve: Simplifying -5 + -16x + x2 = 0 Solving -5 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -16x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -16x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -16x + x2 = 0 + 5 -16x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -16x + x2 = 5 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 = 5 + 64 Reorder the terms: 64 + -16x + x2 = 5 + 64 Combine like terms: 5 + 64 = 69 64 + -16x + x2 = 69 Factor a perfect square on the left side: (x + -8)(x + -8) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -8) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -8 = 8.306623863 Simplifying x + -8 = 8.306623863 Reorder the terms: -8 + x = 8.306623863 Solving -8 + x = 8.306623863 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 = 8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.306623863 + 8 x = 8.306623863 + 8 Combine like terms: 8.306623863 + 8 = 16.306623863 x = 16.306623863 Simplifying x = 16.306623863Subproblem 2
x + -8 = -8.306623863 Simplifying x + -8 = -8.306623863 Reorder the terms: -8 + x = -8.306623863 Solving -8 + x = -8.306623863 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 = -8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.306623863 + 8 x = -8.306623863 + 8 Combine like terms: -8.306623863 + 8 = -0.306623863 x = -0.306623863 Simplifying x = -0.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.306623863, -0.306623863}Solution
x = {16.306623863, -0.306623863}
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