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Simplifying 420 = 7.2x + -0.03x2 Solving 420 = 7.2x + -0.03x2 Solving for variable 'x'. Reorder the terms: 420 + -7.2x + 0.03x2 = 7.2x + -7.2x + -0.03x2 + 0.03x2 Combine like terms: 7.2x + -7.2x = 0.0 420 + -7.2x + 0.03x2 = 0.0 + -0.03x2 + 0.03x2 420 + -7.2x + 0.03x2 = -0.03x2 + 0.03x2 Combine like terms: -0.03x2 + 0.03x2 = 0.00 420 + -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'. 14000 + -240x + x2 = 0 Move the constant term to the right: Add '-14000' to each side of the equation. 14000 + -240x + -14000 + x2 = 0 + -14000 Reorder the terms: 14000 + -14000 + -240x + x2 = 0 + -14000 Combine like terms: 14000 + -14000 = 0 0 + -240x + x2 = 0 + -14000 -240x + x2 = 0 + -14000 Combine like terms: 0 + -14000 = -14000 -240x + x2 = -14000 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 = -14000 + 14400 Reorder the terms: 14400 + -240x + x2 = -14000 + 14400 Combine like terms: -14000 + 14400 = 400 14400 + -240x + x2 = 400 Factor a perfect square on the left side: (x + -120)(x + -120) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (x + -120) equal to 20 and -20.Subproblem 1
x + -120 = 20 Simplifying x + -120 = 20 Reorder the terms: -120 + x = 20 Solving -120 + x = 20 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 = 20 + 120 Combine like terms: -120 + 120 = 0 0 + x = 20 + 120 x = 20 + 120 Combine like terms: 20 + 120 = 140 x = 140 Simplifying x = 140Subproblem 2
x + -120 = -20 Simplifying x + -120 = -20 Reorder the terms: -120 + x = -20 Solving -120 + x = -20 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 = -20 + 120 Combine like terms: -120 + 120 = 0 0 + x = -20 + 120 x = -20 + 120 Combine like terms: -20 + 120 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {140, 100}
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