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Simplifying 7 = 0.0002x2 + -0.316x + 127.9 Reorder the terms: 7 = 127.9 + -0.316x + 0.0002x2 Solving 7 = 127.9 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 7 + -127.9 = -120.9 -120.9 + 0.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2 Reorder the terms: -120.9 + 0.316x + -0.0002x2 = 127.9 + -127.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 127.9 + -127.9 = 0.0 -120.9 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -120.9 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -120.9 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -120.9 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -120.9 + 0.316x + -0.0002x2 = 0.0000 Begin completing the square. Divide all terms by -0.0002 the coefficient of the squared term: Divide each side by '-0.0002'. 604500 + -1580x + x2 = 0 Move the constant term to the right: Add '-604500' to each side of the equation. 604500 + -1580x + -604500 + x2 = 0 + -604500 Reorder the terms: 604500 + -604500 + -1580x + x2 = 0 + -604500 Combine like terms: 604500 + -604500 = 0 0 + -1580x + x2 = 0 + -604500 -1580x + x2 = 0 + -604500 Combine like terms: 0 + -604500 = -604500 -1580x + x2 = -604500 The x term is -1580x. Take half its coefficient (-790). Square it (624100) and add it to both sides. Add '624100' to each side of the equation. -1580x + 624100 + x2 = -604500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -604500 + 624100 Combine like terms: -604500 + 624100 = 19600 624100 + -1580x + x2 = 19600 Factor a perfect square on the left side: (x + -790)(x + -790) = 19600 Calculate the square root of the right side: 140 Break this problem into two subproblems by setting (x + -790) equal to 140 and -140.Subproblem 1
x + -790 = 140 Simplifying x + -790 = 140 Reorder the terms: -790 + x = 140 Solving -790 + x = 140 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = 140 + 790 Combine like terms: -790 + 790 = 0 0 + x = 140 + 790 x = 140 + 790 Combine like terms: 140 + 790 = 930 x = 930 Simplifying x = 930Subproblem 2
x + -790 = -140 Simplifying x + -790 = -140 Reorder the terms: -790 + x = -140 Solving -790 + x = -140 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = -140 + 790 Combine like terms: -790 + 790 = 0 0 + x = -140 + 790 x = -140 + 790 Combine like terms: -140 + 790 = 650 x = 650 Simplifying x = 650Solution
The solution to the problem is based on the solutions from the subproblems. x = {930, 650}
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