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Simplifying 2x2 + -32x = -24 Reorder the terms: -32x + 2x2 = -24 Solving -32x + 2x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + -32x + 2x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + -32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -16x + x2)' equal to zero and attempt to solve: Simplifying 12 + -16x + x2 = 0 Solving 12 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -16x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -16x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -16x + x2 = 0 + -12 -16x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -16x + x2 = -12 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 = -12 + 64 Reorder the terms: 64 + -16x + x2 = -12 + 64 Combine like terms: -12 + 64 = 52 64 + -16x + x2 = 52 Factor a perfect square on the left side: (x + -8)(x + -8) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -8) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -8 = 7.211102551 Simplifying x + -8 = 7.211102551 Reorder the terms: -8 + x = 7.211102551 Solving -8 + x = 7.211102551 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 = 7.211102551 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.211102551 + 8 x = 7.211102551 + 8 Combine like terms: 7.211102551 + 8 = 15.211102551 x = 15.211102551 Simplifying x = 15.211102551Subproblem 2
x + -8 = -7.211102551 Simplifying x + -8 = -7.211102551 Reorder the terms: -8 + x = -7.211102551 Solving -8 + x = -7.211102551 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 = -7.211102551 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.211102551 + 8 x = -7.211102551 + 8 Combine like terms: -7.211102551 + 8 = 0.788897449 x = 0.788897449 Simplifying x = 0.788897449Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.211102551, 0.788897449}Solution
x = {15.211102551, 0.788897449}
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