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Simplifying 9 = -0.08x2 + 1.6x + 2 Reorder the terms: 9 = 2 + 1.6x + -0.08x2 Solving 9 = 2 + 1.6x + -0.08x2 Solving for variable 'x'. Combine like terms: 9 + -2 = 7 7 + -1.6x + 0.08x2 = 2 + 1.6x + -0.08x2 + -2 + -1.6x + 0.08x2 Reorder the terms: 7 + -1.6x + 0.08x2 = 2 + -2 + 1.6x + -1.6x + -0.08x2 + 0.08x2 Combine like terms: 2 + -2 = 0 7 + -1.6x + 0.08x2 = 0 + 1.6x + -1.6x + -0.08x2 + 0.08x2 7 + -1.6x + 0.08x2 = 1.6x + -1.6x + -0.08x2 + 0.08x2 Combine like terms: 1.6x + -1.6x = 0.0 7 + -1.6x + 0.08x2 = 0.0 + -0.08x2 + 0.08x2 7 + -1.6x + 0.08x2 = -0.08x2 + 0.08x2 Combine like terms: -0.08x2 + 0.08x2 = 0.00 7 + -1.6x + 0.08x2 = 0.00 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. 87.5 + -20x + x2 = 0 Move the constant term to the right: Add '-87.5' to each side of the equation. 87.5 + -20x + -87.5 + x2 = 0 + -87.5 Reorder the terms: 87.5 + -87.5 + -20x + x2 = 0 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + -20x + x2 = 0 + -87.5 -20x + x2 = 0 + -87.5 Combine like terms: 0 + -87.5 = -87.5 -20x + x2 = -87.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -87.5 + 100 Reorder the terms: 100 + -20x + x2 = -87.5 + 100 Combine like terms: -87.5 + 100 = 12.5 100 + -20x + x2 = 12.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -10) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -10 = 3.535533906 Simplifying x + -10 = 3.535533906 Reorder the terms: -10 + x = 3.535533906 Solving -10 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 3.535533906 + 10 Combine like terms: -10 + 10 = 0 0 + x = 3.535533906 + 10 x = 3.535533906 + 10 Combine like terms: 3.535533906 + 10 = 13.535533906 x = 13.535533906 Simplifying x = 13.535533906Subproblem 2
x + -10 = -3.535533906 Simplifying x + -10 = -3.535533906 Reorder the terms: -10 + x = -3.535533906 Solving -10 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -3.535533906 + 10 Combine like terms: -10 + 10 = 0 0 + x = -3.535533906 + 10 x = -3.535533906 + 10 Combine like terms: -3.535533906 + 10 = 6.464466094 x = 6.464466094 Simplifying x = 6.464466094Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.535533906, 6.464466094}
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