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Simplifying 0.5x2 + -13x + -96 = 0 Reorder the terms: -96 + -13x + 0.5x2 = 0 Solving -96 + -13x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -192 + -26x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + -26x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -26x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -26x + x2 = 0 + 192 -26x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -26x + x2 = 192 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 = 192 + 169 Reorder the terms: 169 + -26x + x2 = 192 + 169 Combine like terms: 192 + 169 = 361 169 + -26x + x2 = 361 Factor a perfect square on the left side: (x + -13)(x + -13) = 361 Calculate the square root of the right side: 19 Break this problem into two subproblems by setting (x + -13) equal to 19 and -19.Subproblem 1
x + -13 = 19 Simplifying x + -13 = 19 Reorder the terms: -13 + x = 19 Solving -13 + x = 19 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 = 19 + 13 Combine like terms: -13 + 13 = 0 0 + x = 19 + 13 x = 19 + 13 Combine like terms: 19 + 13 = 32 x = 32 Simplifying x = 32Subproblem 2
x + -13 = -19 Simplifying x + -13 = -19 Reorder the terms: -13 + x = -19 Solving -13 + x = -19 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 = -19 + 13 Combine like terms: -13 + 13 = 0 0 + x = -19 + 13 x = -19 + 13 Combine like terms: -19 + 13 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {32, -6}
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