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Simplifying 2x2 + -8x + -36 = 0 Reorder the terms: -36 + -8x + 2x2 = 0 Solving -36 + -8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -4x + x2)' equal to zero and attempt to solve: Simplifying -18 + -4x + x2 = 0 Solving -18 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -4x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -4x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -4x + x2 = 0 + 18 -4x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -4x + x2 = 18 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 18 + 4 Reorder the terms: 4 + -4x + x2 = 18 + 4 Combine like terms: 18 + 4 = 22 4 + -4x + x2 = 22 Factor a perfect square on the left side: (x + -2)(x + -2) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -2) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -2 = 4.69041576 Simplifying x + -2 = 4.69041576 Reorder the terms: -2 + x = 4.69041576 Solving -2 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.69041576 + 2 x = 4.69041576 + 2 Combine like terms: 4.69041576 + 2 = 6.69041576 x = 6.69041576 Simplifying x = 6.69041576Subproblem 2
x + -2 = -4.69041576 Simplifying x + -2 = -4.69041576 Reorder the terms: -2 + x = -4.69041576 Solving -2 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.69041576 + 2 x = -4.69041576 + 2 Combine like terms: -4.69041576 + 2 = -2.69041576 x = -2.69041576 Simplifying x = -2.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.69041576, -2.69041576}Solution
x = {6.69041576, -2.69041576}
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