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Simplifying 2(X2 + -2X + -60) = 0 Reorder the terms: 2(-60 + -2X + X2) = 0 (-60 * 2 + -2X * 2 + X2 * 2) = 0 (-120 + -4X + 2X2) = 0 Solving -120 + -4X + 2X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -2X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + -2X + X2)' equal to zero and attempt to solve: Simplifying -60 + -2X + X2 = 0 Solving -60 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -2X + 60 + X2 = 0 + 60 Reorder the terms: -60 + 60 + -2X + X2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -2X + X2 = 0 + 60 -2X + X2 = 0 + 60 Combine like terms: 0 + 60 = 60 -2X + X2 = 60 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 60 + 1 Reorder the terms: 1 + -2X + X2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + -2X + X2 = 61 Factor a perfect square on the left side: (X + -1)(X + -1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (X + -1) equal to 7.810249676 and -7.810249676.Subproblem 1
X + -1 = 7.810249676 Simplifying X + -1 = 7.810249676 Reorder the terms: -1 + X = 7.810249676 Solving -1 + X = 7.810249676 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + X = 7.810249676 + 1 X = 7.810249676 + 1 Combine like terms: 7.810249676 + 1 = 8.810249676 X = 8.810249676 Simplifying X = 8.810249676Subproblem 2
X + -1 = -7.810249676 Simplifying X + -1 = -7.810249676 Reorder the terms: -1 + X = -7.810249676 Solving -1 + X = -7.810249676 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + X = -7.810249676 + 1 X = -7.810249676 + 1 Combine like terms: -7.810249676 + 1 = -6.810249676 X = -6.810249676 Simplifying X = -6.810249676Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.810249676, -6.810249676}Solution
X = {8.810249676, -6.810249676}
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