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Simplifying 5.5x + -0.025x2 = 180 Solving 5.5x + -0.025x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 5.5x + -0.025x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 5.5x + -0.025x2 = 0 Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. 7200 + -220x + x2 = 0 Move the constant term to the right: Add '-7200' to each side of the equation. 7200 + -220x + -7200 + x2 = 0 + -7200 Reorder the terms: 7200 + -7200 + -220x + x2 = 0 + -7200 Combine like terms: 7200 + -7200 = 0 0 + -220x + x2 = 0 + -7200 -220x + x2 = 0 + -7200 Combine like terms: 0 + -7200 = -7200 -220x + x2 = -7200 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -7200 + 12100 Reorder the terms: 12100 + -220x + x2 = -7200 + 12100 Combine like terms: -7200 + 12100 = 4900 12100 + -220x + x2 = 4900 Factor a perfect square on the left side: (x + -110)(x + -110) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (x + -110) equal to 70 and -70.Subproblem 1
x + -110 = 70 Simplifying x + -110 = 70 Reorder the terms: -110 + x = 70 Solving -110 + x = 70 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 70 + 110 Combine like terms: -110 + 110 = 0 0 + x = 70 + 110 x = 70 + 110 Combine like terms: 70 + 110 = 180 x = 180 Simplifying x = 180Subproblem 2
x + -110 = -70 Simplifying x + -110 = -70 Reorder the terms: -110 + x = -70 Solving -110 + x = -70 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -70 + 110 Combine like terms: -110 + 110 = 0 0 + x = -70 + 110 x = -70 + 110 Combine like terms: -70 + 110 = 40 x = 40 Simplifying x = 40Solution
The solution to the problem is based on the solutions from the subproblems. x = {180, 40}
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