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Simplifying -0.005x2 + 0.17x + 3 = 3.6 Reorder the terms: 3 + 0.17x + -0.005x2 = 3.6 Solving 3 + 0.17x + -0.005x2 = 3.6 Solving for variable 'x'. Reorder the terms: 3 + -3.6 + 0.17x + -0.005x2 = 3.6 + -3.6 Combine like terms: 3 + -3.6 = -0.6 -0.6 + 0.17x + -0.005x2 = 3.6 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 -0.6 + 0.17x + -0.005x2 = 0.0 Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. 120 + -34x + x2 = 0 Move the constant term to the right: Add '-120' to each side of the equation. 120 + -34x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -34x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -34x + x2 = 0 + -120 -34x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -34x + x2 = -120 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -120 + 289 Reorder the terms: 289 + -34x + x2 = -120 + 289 Combine like terms: -120 + 289 = 169 289 + -34x + x2 = 169 Factor a perfect square on the left side: (x + -17)(x + -17) = 169 Calculate the square root of the right side: 13 Break this problem into two subproblems by setting (x + -17) equal to 13 and -13.Subproblem 1
x + -17 = 13 Simplifying x + -17 = 13 Reorder the terms: -17 + x = 13 Solving -17 + x = 13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 13 + 17 Combine like terms: -17 + 17 = 0 0 + x = 13 + 17 x = 13 + 17 Combine like terms: 13 + 17 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -17 = -13 Simplifying x + -17 = -13 Reorder the terms: -17 + x = -13 Solving -17 + x = -13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -13 + 17 Combine like terms: -17 + 17 = 0 0 + x = -13 + 17 x = -13 + 17 Combine like terms: -13 + 17 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, 4}
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