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Simplifying -2(x2 + 60x + -16140) = 0 Reorder the terms: -2(-16140 + 60x + x2) = 0 (-16140 * -2 + 60x * -2 + x2 * -2) = 0 (32280 + -120x + -2x2) = 0 Solving 32280 + -120x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16140 + -60x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16140 + -60x + -1x2)' equal to zero and attempt to solve: Simplifying 16140 + -60x + -1x2 = 0 Solving 16140 + -60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16140 + 60x + x2 = 0 Move the constant term to the right: Add '16140' to each side of the equation. -16140 + 60x + 16140 + x2 = 0 + 16140 Reorder the terms: -16140 + 16140 + 60x + x2 = 0 + 16140 Combine like terms: -16140 + 16140 = 0 0 + 60x + x2 = 0 + 16140 60x + x2 = 0 + 16140 Combine like terms: 0 + 16140 = 16140 60x + x2 = 16140 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 16140 + 900 Reorder the terms: 900 + 60x + x2 = 16140 + 900 Combine like terms: 16140 + 900 = 17040 900 + 60x + x2 = 17040 Factor a perfect square on the left side: (x + 30)(x + 30) = 17040 Calculate the square root of the right side: 130.537350977 Break this problem into two subproblems by setting (x + 30) equal to 130.537350977 and -130.537350977.Subproblem 1
x + 30 = 130.537350977 Simplifying x + 30 = 130.537350977 Reorder the terms: 30 + x = 130.537350977 Solving 30 + x = 130.537350977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 130.537350977 + -30 Combine like terms: 30 + -30 = 0 0 + x = 130.537350977 + -30 x = 130.537350977 + -30 Combine like terms: 130.537350977 + -30 = 100.537350977 x = 100.537350977 Simplifying x = 100.537350977Subproblem 2
x + 30 = -130.537350977 Simplifying x + 30 = -130.537350977 Reorder the terms: 30 + x = -130.537350977 Solving 30 + x = -130.537350977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -130.537350977 + -30 Combine like terms: 30 + -30 = 0 0 + x = -130.537350977 + -30 x = -130.537350977 + -30 Combine like terms: -130.537350977 + -30 = -160.537350977 x = -160.537350977 Simplifying x = -160.537350977Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.537350977, -160.537350977}Solution
x = {100.537350977, -160.537350977}
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