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Simplifying -0.5x2 + 33.528x + -100 = 0 Reorder the terms: -100 + 33.528x + -0.5x2 = 0 Solving -100 + 33.528x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 200 + -67.056x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -67.056x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -67.056x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -67.056x + x2 = 0 + -200 -67.056x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -67.056x + x2 = -200 The x term is -67.056x. Take half its coefficient (-33.528). Square it (1124.126784) and add it to both sides. Add '1124.126784' to each side of the equation. -67.056x + 1124.126784 + x2 = -200 + 1124.126784 Reorder the terms: 1124.126784 + -67.056x + x2 = -200 + 1124.126784 Combine like terms: -200 + 1124.126784 = 924.126784 1124.126784 + -67.056x + x2 = 924.126784 Factor a perfect square on the left side: (x + -33.528)(x + -33.528) = 924.126784 Calculate the square root of the right side: 30.399453679 Break this problem into two subproblems by setting (x + -33.528) equal to 30.399453679 and -30.399453679.Subproblem 1
x + -33.528 = 30.399453679 Simplifying x + -33.528 = 30.399453679 Reorder the terms: -33.528 + x = 30.399453679 Solving -33.528 + x = 30.399453679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.528' to each side of the equation. -33.528 + 33.528 + x = 30.399453679 + 33.528 Combine like terms: -33.528 + 33.528 = 0.000 0.000 + x = 30.399453679 + 33.528 x = 30.399453679 + 33.528 Combine like terms: 30.399453679 + 33.528 = 63.927453679 x = 63.927453679 Simplifying x = 63.927453679Subproblem 2
x + -33.528 = -30.399453679 Simplifying x + -33.528 = -30.399453679 Reorder the terms: -33.528 + x = -30.399453679 Solving -33.528 + x = -30.399453679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.528' to each side of the equation. -33.528 + 33.528 + x = -30.399453679 + 33.528 Combine like terms: -33.528 + 33.528 = 0.000 0.000 + x = -30.399453679 + 33.528 x = -30.399453679 + 33.528 Combine like terms: -30.399453679 + 33.528 = 3.128546321 x = 3.128546321 Simplifying x = 3.128546321Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.927453679, 3.128546321}
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