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Simplifying 0.01x2 + -1.9x = -88 Reorder the terms: -1.9x + 0.01x2 = -88 Solving -1.9x + 0.01x2 = -88 Solving for variable 'x'. Reorder the terms: 88 + -1.9x + 0.01x2 = -88 + 88 Combine like terms: -88 + 88 = 0 88 + -1.9x + 0.01x2 = 0 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 8800 + -190x + x2 = 0 Move the constant term to the right: Add '-8800' to each side of the equation. 8800 + -190x + -8800 + x2 = 0 + -8800 Reorder the terms: 8800 + -8800 + -190x + x2 = 0 + -8800 Combine like terms: 8800 + -8800 = 0 0 + -190x + x2 = 0 + -8800 -190x + x2 = 0 + -8800 Combine like terms: 0 + -8800 = -8800 -190x + x2 = -8800 The x term is -190x. Take half its coefficient (-95). Square it (9025) and add it to both sides. Add '9025' to each side of the equation. -190x + 9025 + x2 = -8800 + 9025 Reorder the terms: 9025 + -190x + x2 = -8800 + 9025 Combine like terms: -8800 + 9025 = 225 9025 + -190x + x2 = 225 Factor a perfect square on the left side: (x + -95)(x + -95) = 225 Calculate the square root of the right side: 15 Break this problem into two subproblems by setting (x + -95) equal to 15 and -15.Subproblem 1
x + -95 = 15 Simplifying x + -95 = 15 Reorder the terms: -95 + x = 15 Solving -95 + x = 15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = 15 + 95 Combine like terms: -95 + 95 = 0 0 + x = 15 + 95 x = 15 + 95 Combine like terms: 15 + 95 = 110 x = 110 Simplifying x = 110Subproblem 2
x + -95 = -15 Simplifying x + -95 = -15 Reorder the terms: -95 + x = -15 Solving -95 + x = -15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = -15 + 95 Combine like terms: -95 + 95 = 0 0 + x = -15 + 95 x = -15 + 95 Combine like terms: -15 + 95 = 80 x = 80 Simplifying x = 80Solution
The solution to the problem is based on the solutions from the subproblems. x = {110, 80}
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