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Simplifying -0.01x2 + 1.2x + -20 = 7 Reorder the terms: -20 + 1.2x + -0.01x2 = 7 Solving -20 + 1.2x + -0.01x2 = 7 Solving for variable 'x'. Reorder the terms: -20 + -7 + 1.2x + -0.01x2 = 7 + -7 Combine like terms: -20 + -7 = -27 -27 + 1.2x + -0.01x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -27 + 1.2x + -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'. 2700 + -120x + x2 = 0 Move the constant term to the right: Add '-2700' to each side of the equation. 2700 + -120x + -2700 + x2 = 0 + -2700 Reorder the terms: 2700 + -2700 + -120x + x2 = 0 + -2700 Combine like terms: 2700 + -2700 = 0 0 + -120x + x2 = 0 + -2700 -120x + x2 = 0 + -2700 Combine like terms: 0 + -2700 = -2700 -120x + x2 = -2700 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -2700 + 3600 Reorder the terms: 3600 + -120x + x2 = -2700 + 3600 Combine like terms: -2700 + 3600 = 900 3600 + -120x + x2 = 900 Factor a perfect square on the left side: (x + -60)(x + -60) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + -60) equal to 30 and -30.Subproblem 1
x + -60 = 30 Simplifying x + -60 = 30 Reorder the terms: -60 + x = 30 Solving -60 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 30 + 60 Combine like terms: -60 + 60 = 0 0 + x = 30 + 60 x = 30 + 60 Combine like terms: 30 + 60 = 90 x = 90 Simplifying x = 90Subproblem 2
x + -60 = -30 Simplifying x + -60 = -30 Reorder the terms: -60 + x = -30 Solving -60 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -30 + 60 Combine like terms: -60 + 60 = 0 0 + x = -30 + 60 x = -30 + 60 Combine like terms: -30 + 60 = 30 x = 30 Simplifying x = 30Solution
The solution to the problem is based on the solutions from the subproblems. x = {90, 30}
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