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Simplifying 50x(42 + -1x) = 1500 (42 * 50x + -1x * 50x) = 1500 (2100x + -50x2) = 1500 Solving 2100x + -50x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 2100x + -50x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 2100x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-30 + 42x + -1x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-30 + 42x + -1x2)' equal to zero and attempt to solve: Simplifying -30 + 42x + -1x2 = 0 Solving -30 + 42x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -42x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -42x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -42x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -42x + x2 = 0 + -30 -42x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -42x + x2 = -30 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -30 + 441 Reorder the terms: 441 + -42x + x2 = -30 + 441 Combine like terms: -30 + 441 = 411 441 + -42x + x2 = 411 Factor a perfect square on the left side: (x + -21)(x + -21) = 411 Calculate the square root of the right side: 20.273134933 Break this problem into two subproblems by setting (x + -21) equal to 20.273134933 and -20.273134933.Subproblem 1
x + -21 = 20.273134933 Simplifying x + -21 = 20.273134933 Reorder the terms: -21 + x = 20.273134933 Solving -21 + x = 20.273134933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 20.273134933 + 21 Combine like terms: -21 + 21 = 0 0 + x = 20.273134933 + 21 x = 20.273134933 + 21 Combine like terms: 20.273134933 + 21 = 41.273134933 x = 41.273134933 Simplifying x = 41.273134933Subproblem 2
x + -21 = -20.273134933 Simplifying x + -21 = -20.273134933 Reorder the terms: -21 + x = -20.273134933 Solving -21 + x = -20.273134933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -20.273134933 + 21 Combine like terms: -21 + 21 = 0 0 + x = -20.273134933 + 21 x = -20.273134933 + 21 Combine like terms: -20.273134933 + 21 = 0.726865067 x = 0.726865067 Simplifying x = 0.726865067Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.273134933, 0.726865067}Solution
x = {41.273134933, 0.726865067}
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