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Simplifying 20 = -0.2(x * x) + 7.2x + 1.5 Multiply x * x 20 = -0.2(x2) + 7.2x + 1.5 Reorder the terms: 20 = 1.5 + 7.2x + -0.2x2 Solving 20 = 1.5 + 7.2x + -0.2x2 Solving for variable 'x'. Combine like terms: 20 + -1.5 = 18.5 18.5 + -7.2x + 0.2x2 = 1.5 + 7.2x + -0.2x2 + -1.5 + -7.2x + 0.2x2 Reorder the terms: 18.5 + -7.2x + 0.2x2 = 1.5 + -1.5 + 7.2x + -7.2x + -0.2x2 + 0.2x2 Combine like terms: 1.5 + -1.5 = 0.0 18.5 + -7.2x + 0.2x2 = 0.0 + 7.2x + -7.2x + -0.2x2 + 0.2x2 18.5 + -7.2x + 0.2x2 = 7.2x + -7.2x + -0.2x2 + 0.2x2 Combine like terms: 7.2x + -7.2x = 0.0 18.5 + -7.2x + 0.2x2 = 0.0 + -0.2x2 + 0.2x2 18.5 + -7.2x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 18.5 + -7.2x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 92.5 + -36x + x2 = 0 Move the constant term to the right: Add '-92.5' to each side of the equation. 92.5 + -36x + -92.5 + x2 = 0 + -92.5 Reorder the terms: 92.5 + -92.5 + -36x + x2 = 0 + -92.5 Combine like terms: 92.5 + -92.5 = 0.0 0.0 + -36x + x2 = 0 + -92.5 -36x + x2 = 0 + -92.5 Combine like terms: 0 + -92.5 = -92.5 -36x + x2 = -92.5 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -92.5 + 324 Reorder the terms: 324 + -36x + x2 = -92.5 + 324 Combine like terms: -92.5 + 324 = 231.5 324 + -36x + x2 = 231.5 Factor a perfect square on the left side: (x + -18)(x + -18) = 231.5 Calculate the square root of the right side: 15.215124055 Break this problem into two subproblems by setting (x + -18) equal to 15.215124055 and -15.215124055.Subproblem 1
x + -18 = 15.215124055 Simplifying x + -18 = 15.215124055 Reorder the terms: -18 + x = 15.215124055 Solving -18 + x = 15.215124055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 15.215124055 + 18 Combine like terms: -18 + 18 = 0 0 + x = 15.215124055 + 18 x = 15.215124055 + 18 Combine like terms: 15.215124055 + 18 = 33.215124055 x = 33.215124055 Simplifying x = 33.215124055Subproblem 2
x + -18 = -15.215124055 Simplifying x + -18 = -15.215124055 Reorder the terms: -18 + x = -15.215124055 Solving -18 + x = -15.215124055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -15.215124055 + 18 Combine like terms: -18 + 18 = 0 0 + x = -15.215124055 + 18 x = -15.215124055 + 18 Combine like terms: -15.215124055 + 18 = 2.784875945 x = 2.784875945 Simplifying x = 2.784875945Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.215124055, 2.784875945}
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