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Simplifying x(20 + -1x) = 93.75 (20 * x + -1x * x) = 93.75 (20x + -1x2) = 93.75 Solving 20x + -1x2 = 93.75 Solving for variable 'x'. Reorder the terms: -93.75 + 20x + -1x2 = 93.75 + -93.75 Combine like terms: 93.75 + -93.75 = 0.00 -93.75 + 20x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 93.75 + -20x + x2 = 0.00 Move the constant term to the right: Add '-93.75' to each side of the equation. 93.75 + -20x + -93.75 + x2 = 0.00 + -93.75 Reorder the terms: 93.75 + -93.75 + -20x + x2 = 0.00 + -93.75 Combine like terms: 93.75 + -93.75 = 0.00 0.00 + -20x + x2 = 0.00 + -93.75 -20x + x2 = 0.00 + -93.75 Combine like terms: 0.00 + -93.75 = -93.75 -20x + x2 = -93.75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -93.75 + 100 Reorder the terms: 100 + -20x + x2 = -93.75 + 100 Combine like terms: -93.75 + 100 = 6.25 100 + -20x + x2 = 6.25 Factor a perfect square on the left side: (x + -10)(x + -10) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -10) equal to 2.5 and -2.5.Subproblem 1
x + -10 = 2.5 Simplifying x + -10 = 2.5 Reorder the terms: -10 + x = 2.5 Solving -10 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 2.5 + 10 Combine like terms: -10 + 10 = 0 0 + x = 2.5 + 10 x = 2.5 + 10 Combine like terms: 2.5 + 10 = 12.5 x = 12.5 Simplifying x = 12.5Subproblem 2
x + -10 = -2.5 Simplifying x + -10 = -2.5 Reorder the terms: -10 + x = -2.5 Solving -10 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -2.5 + 10 Combine like terms: -10 + 10 = 0 0 + x = -2.5 + 10 x = -2.5 + 10 Combine like terms: -2.5 + 10 = 7.5 x = 7.5 Simplifying x = 7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5, 7.5}
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