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Simplifying (10 + 2x)(15 + 2x) = 250 Multiply (10 + 2x) * (15 + 2x) (10(15 + 2x) + 2x * (15 + 2x)) = 250 ((15 * 10 + 2x * 10) + 2x * (15 + 2x)) = 250 ((150 + 20x) + 2x * (15 + 2x)) = 250 (150 + 20x + (15 * 2x + 2x * 2x)) = 250 (150 + 20x + (30x + 4x2)) = 250 Combine like terms: 20x + 30x = 50x (150 + 50x + 4x2) = 250 Solving 150 + 50x + 4x2 = 250 Solving for variable 'x'. Reorder the terms: 150 + -250 + 50x + 4x2 = 250 + -250 Combine like terms: 150 + -250 = -100 -100 + 50x + 4x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -100 + 50x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 25x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 25x + 2x2)' equal to zero and attempt to solve: Simplifying -50 + 25x + 2x2 = 0 Solving -50 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 12.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 12.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 12.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 12.5x + x2 = 0 + 25 12.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 12.5x + x2 = 25 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 25 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 25 + 39.0625 Combine like terms: 25 + 39.0625 = 64.0625 39.0625 + 12.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + 6.25) equal to 8.003905297 and -8.003905297.Subproblem 1
x + 6.25 = 8.003905297 Simplifying x + 6.25 = 8.003905297 Reorder the terms: 6.25 + x = 8.003905297 Solving 6.25 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 8.003905297 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 8.003905297 + -6.25 x = 8.003905297 + -6.25 Combine like terms: 8.003905297 + -6.25 = 1.753905297 x = 1.753905297 Simplifying x = 1.753905297Subproblem 2
x + 6.25 = -8.003905297 Simplifying x + 6.25 = -8.003905297 Reorder the terms: 6.25 + x = -8.003905297 Solving 6.25 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -8.003905297 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -8.003905297 + -6.25 x = -8.003905297 + -6.25 Combine like terms: -8.003905297 + -6.25 = -14.253905297 x = -14.253905297 Simplifying x = -14.253905297Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.753905297, -14.253905297}Solution
x = {1.753905297, -14.253905297}
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