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Simplifying -0.01x2 + 0.28x + 8.68 = 9.2 Reorder the terms: 8.68 + 0.28x + -0.01x2 = 9.2 Solving 8.68 + 0.28x + -0.01x2 = 9.2 Solving for variable 'x'. Reorder the terms: 8.68 + -9.2 + 0.28x + -0.01x2 = 9.2 + -9.2 Combine like terms: 8.68 + -9.2 = -0.52 -0.52 + 0.28x + -0.01x2 = 9.2 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 -0.52 + 0.28x + -0.01x2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 52 + -28x + x2 = 0 Move the constant term to the right: Add '-52' to each side of the equation. 52 + -28x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -28x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -28x + x2 = 0 + -52 -28x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -28x + x2 = -52 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -52 + 196 Reorder the terms: 196 + -28x + x2 = -52 + 196 Combine like terms: -52 + 196 = 144 196 + -28x + x2 = 144 Factor a perfect square on the left side: (x + -14)(x + -14) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -14) equal to 12 and -12.Subproblem 1
x + -14 = 12 Simplifying x + -14 = 12 Reorder the terms: -14 + x = 12 Solving -14 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12 + 14 x = 12 + 14 Combine like terms: 12 + 14 = 26 x = 26 Simplifying x = 26Subproblem 2
x + -14 = -12 Simplifying x + -14 = -12 Reorder the terms: -14 + x = -12 Solving -14 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12 + 14 x = -12 + 14 Combine like terms: -12 + 14 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {26, 2}
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