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Simplifying 429 = 7.2x + -0.03x2 Solving 429 = 7.2x + -0.03x2 Solving for variable 'x'. Reorder the terms: 429 + -7.2x + 0.03x2 = 7.2x + -7.2x + -0.03x2 + 0.03x2 Combine like terms: 7.2x + -7.2x = 0.0 429 + -7.2x + 0.03x2 = 0.0 + -0.03x2 + 0.03x2 429 + -7.2x + 0.03x2 = -0.03x2 + 0.03x2 Combine like terms: -0.03x2 + 0.03x2 = 0.00 429 + -7.2x + 0.03x2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 14300 + -240x + x2 = 0 Move the constant term to the right: Add '-14300' to each side of the equation. 14300 + -240x + -14300 + x2 = 0 + -14300 Reorder the terms: 14300 + -14300 + -240x + x2 = 0 + -14300 Combine like terms: 14300 + -14300 = 0 0 + -240x + x2 = 0 + -14300 -240x + x2 = 0 + -14300 Combine like terms: 0 + -14300 = -14300 -240x + x2 = -14300 The x term is -240x. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240x + 14400 + x2 = -14300 + 14400 Reorder the terms: 14400 + -240x + x2 = -14300 + 14400 Combine like terms: -14300 + 14400 = 100 14400 + -240x + x2 = 100 Factor a perfect square on the left side: (x + -120)(x + -120) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -120) equal to 10 and -10.Subproblem 1
x + -120 = 10 Simplifying x + -120 = 10 Reorder the terms: -120 + x = 10 Solving -120 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 10 + 120 Combine like terms: -120 + 120 = 0 0 + x = 10 + 120 x = 10 + 120 Combine like terms: 10 + 120 = 130 x = 130 Simplifying x = 130Subproblem 2
x + -120 = -10 Simplifying x + -120 = -10 Reorder the terms: -120 + x = -10 Solving -120 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = -10 + 120 Combine like terms: -120 + 120 = 0 0 + x = -10 + 120 x = -10 + 120 Combine like terms: -10 + 120 = 110 x = 110 Simplifying x = 110Solution
The solution to the problem is based on the solutions from the subproblems. x = {130, 110}
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