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Simplifying (30 + -2x)(15 + -2x) = 200 Multiply (30 + -2x) * (15 + -2x) (30(15 + -2x) + -2x * (15 + -2x)) = 200 ((15 * 30 + -2x * 30) + -2x * (15 + -2x)) = 200 ((450 + -60x) + -2x * (15 + -2x)) = 200 (450 + -60x + (15 * -2x + -2x * -2x)) = 200 (450 + -60x + (-30x + 4x2)) = 200 Combine like terms: -60x + -30x = -90x (450 + -90x + 4x2) = 200 Solving 450 + -90x + 4x2 = 200 Solving for variable 'x'. Reorder the terms: 450 + -200 + -90x + 4x2 = 200 + -200 Combine like terms: 450 + -200 = 250 250 + -90x + 4x2 = 200 + -200 Combine like terms: 200 + -200 = 0 250 + -90x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(125 + -45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(125 + -45x + 2x2)' equal to zero and attempt to solve: Simplifying 125 + -45x + 2x2 = 0 Solving 125 + -45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 62.5 + -22.5x + x2 = 0 Move the constant term to the right: Add '-62.5' to each side of the equation. 62.5 + -22.5x + -62.5 + x2 = 0 + -62.5 Reorder the terms: 62.5 + -62.5 + -22.5x + x2 = 0 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + -22.5x + x2 = 0 + -62.5 -22.5x + x2 = 0 + -62.5 Combine like terms: 0 + -62.5 = -62.5 -22.5x + x2 = -62.5 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = -62.5 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -62.5 + 126.5625 Combine like terms: -62.5 + 126.5625 = 64.0625 126.5625 + -22.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + -11.25) equal to 8.003905297 and -8.003905297.Subproblem 1
x + -11.25 = 8.003905297 Simplifying x + -11.25 = 8.003905297 Reorder the terms: -11.25 + x = 8.003905297 Solving -11.25 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 8.003905297 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 8.003905297 + 11.25 x = 8.003905297 + 11.25 Combine like terms: 8.003905297 + 11.25 = 19.253905297 x = 19.253905297 Simplifying x = 19.253905297Subproblem 2
x + -11.25 = -8.003905297 Simplifying x + -11.25 = -8.003905297 Reorder the terms: -11.25 + x = -8.003905297 Solving -11.25 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -8.003905297 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -8.003905297 + 11.25 x = -8.003905297 + 11.25 Combine like terms: -8.003905297 + 11.25 = 3.246094703 x = 3.246094703 Simplifying x = 3.246094703Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.253905297, 3.246094703}Solution
x = {19.253905297, 3.246094703}
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