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Simplifying 2x2 + 12x = 64 Reorder the terms: 12x + 2x2 = 64 Solving 12x + 2x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 12x + 2x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 6x + x2)' equal to zero and attempt to solve: Simplifying -32 + 6x + x2 = 0 Solving -32 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 6x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 6x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 6x + x2 = 0 + 32 6x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 6x + x2 = 32 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 32 + 9 Reorder the terms: 9 + 6x + x2 = 32 + 9 Combine like terms: 32 + 9 = 41 9 + 6x + x2 = 41 Factor a perfect square on the left side: (x + 3)(x + 3) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 3) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 3 = 6.403124237 Simplifying x + 3 = 6.403124237 Reorder the terms: 3 + x = 6.403124237 Solving 3 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.403124237 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.403124237 + -3 x = 6.403124237 + -3 Combine like terms: 6.403124237 + -3 = 3.403124237 x = 3.403124237 Simplifying x = 3.403124237Subproblem 2
x + 3 = -6.403124237 Simplifying x + 3 = -6.403124237 Reorder the terms: 3 + x = -6.403124237 Solving 3 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.403124237 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.403124237 + -3 x = -6.403124237 + -3 Combine like terms: -6.403124237 + -3 = -9.403124237 x = -9.403124237 Simplifying x = -9.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.403124237, -9.403124237}Solution
x = {3.403124237, -9.403124237}
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