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Simplifying -0.01x2 + 0.26x + 7.60 = 9.2 Reorder the terms: 7.60 + 0.26x + -0.01x2 = 9.2 Solving 7.60 + 0.26x + -0.01x2 = 9.2 Solving for variable 'x'. Reorder the terms: 7.60 + -9.2 + 0.26x + -0.01x2 = 9.2 + -9.2 Combine like terms: 7.60 + -9.2 = -1.6 -1.6 + 0.26x + -0.01x2 = 9.2 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 -1.6 + 0.26x + -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'. 160 + -26x + x2 = 0 Move the constant term to the right: Add '-160' to each side of the equation. 160 + -26x + -160 + x2 = 0 + -160 Reorder the terms: 160 + -160 + -26x + x2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + -26x + x2 = 0 + -160 -26x + x2 = 0 + -160 Combine like terms: 0 + -160 = -160 -26x + x2 = -160 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -160 + 169 Reorder the terms: 169 + -26x + x2 = -160 + 169 Combine like terms: -160 + 169 = 9 169 + -26x + x2 = 9 Factor a perfect square on the left side: (x + -13)(x + -13) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -13) equal to 3 and -3.Subproblem 1
x + -13 = 3 Simplifying x + -13 = 3 Reorder the terms: -13 + x = 3 Solving -13 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 3 + 13 Combine like terms: -13 + 13 = 0 0 + x = 3 + 13 x = 3 + 13 Combine like terms: 3 + 13 = 16 x = 16 Simplifying x = 16Subproblem 2
x + -13 = -3 Simplifying x + -13 = -3 Reorder the terms: -13 + x = -3 Solving -13 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -3 + 13 Combine like terms: -13 + 13 = 0 0 + x = -3 + 13 x = -3 + 13 Combine like terms: -3 + 13 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, 10}
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