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Simplifying 280 = (2x + 2) * x Reorder the terms: 280 = (2 + 2x) * x Reorder the terms for easier multiplication: 280 = x(2 + 2x) 280 = (2 * x + 2x * x) 280 = (2x + 2x2) Solving 280 = 2x + 2x2 Solving for variable 'x'. Reorder the terms: 280 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 280 + -2x + -2x2 = 0 + 2x2 + -2x2 280 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 280 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(140 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(140 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 140 + -1x + -1x2 = 0 Solving 140 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + x + x2 = 0 + 140 x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 x + x2 = 140 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 140 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 140 + 0.25 Combine like terms: 140 + 0.25 = 140.25 1.25 + x2 = 140.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 0.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 0.5 = 11.842719282 Simplifying x + 0.5 = 11.842719282 Reorder the terms: 0.5 + x = 11.842719282 Solving 0.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.842719282 + -0.5 x = 11.842719282 + -0.5 Combine like terms: 11.842719282 + -0.5 = 11.342719282 x = 11.342719282 Simplifying x = 11.342719282Subproblem 2
x + 0.5 = -11.842719282 Simplifying x + 0.5 = -11.842719282 Reorder the terms: 0.5 + x = -11.842719282 Solving 0.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.842719282 + -0.5 x = -11.842719282 + -0.5 Combine like terms: -11.842719282 + -0.5 = -12.342719282 x = -12.342719282 Simplifying x = -12.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.342719282, -12.342719282}Solution
x = {11.342719282, -12.342719282}
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