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Simplifying -36 + x2 + -20x = 36 + -1x2 Reorder the terms: -36 + -20x + x2 = 36 + -1x2 Solving -36 + -20x + x2 = 36 + -1x2 Solving for variable 'x'. Reorder the terms: -36 + -36 + -20x + x2 + x2 = 36 + -1x2 + -36 + x2 Combine like terms: -36 + -36 = -72 -72 + -20x + x2 + x2 = 36 + -1x2 + -36 + x2 Combine like terms: x2 + x2 = 2x2 -72 + -20x + 2x2 = 36 + -1x2 + -36 + x2 Reorder the terms: -72 + -20x + 2x2 = 36 + -36 + -1x2 + x2 Combine like terms: 36 + -36 = 0 -72 + -20x + 2x2 = 0 + -1x2 + x2 -72 + -20x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -72 + -20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + -10x + x2)' equal to zero and attempt to solve: Simplifying -36 + -10x + x2 = 0 Solving -36 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -10x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -10x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -10x + x2 = 0 + 36 -10x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -10x + x2 = 36 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 36 + 25 Reorder the terms: 25 + -10x + x2 = 36 + 25 Combine like terms: 36 + 25 = 61 25 + -10x + x2 = 61 Factor a perfect square on the left side: (x + -5)(x + -5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -5) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -5 = 7.810249676 Simplifying x + -5 = 7.810249676 Reorder the terms: -5 + x = 7.810249676 Solving -5 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.810249676 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.810249676 + 5 x = 7.810249676 + 5 Combine like terms: 7.810249676 + 5 = 12.810249676 x = 12.810249676 Simplifying x = 12.810249676Subproblem 2
x + -5 = -7.810249676 Simplifying x + -5 = -7.810249676 Reorder the terms: -5 + x = -7.810249676 Solving -5 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.810249676 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.810249676 + 5 x = -7.810249676 + 5 Combine like terms: -7.810249676 + 5 = -2.810249676 x = -2.810249676 Simplifying x = -2.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.810249676, -2.810249676}Solution
x = {12.810249676, -2.810249676}
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