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Simplifying 2x2 + -12x + 36 = 32 Reorder the terms: 36 + -12x + 2x2 = 32 Solving 36 + -12x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: 36 + -32 + -12x + 2x2 = 32 + -32 Combine like terms: 36 + -32 = 4 4 + -12x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 4 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -6x + x2)' equal to zero and attempt to solve: Simplifying 2 + -6x + x2 = 0 Solving 2 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x + x2 = 0 + -2 -6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x + x2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6x + x2 = 7 Factor a perfect square on the left side: (x + -3)(x + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311Subproblem 2
x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}Solution
x = {5.645751311, 0.354248689}
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