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Simplifying 0.5x2 + -13x + 15 = 0 Reorder the terms: 15 + -13x + 0.5x2 = 0 Solving 15 + -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'. 30 + -26x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -26x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -26x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -26x + x2 = 0 + -30 -26x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -26x + x2 = -30 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 = -30 + 169 Reorder the terms: 169 + -26x + x2 = -30 + 169 Combine like terms: -30 + 169 = 139 169 + -26x + x2 = 139 Factor a perfect square on the left side: (x + -13)(x + -13) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + -13) equal to 11.789826123 and -11.789826123.Subproblem 1
x + -13 = 11.789826123 Simplifying x + -13 = 11.789826123 Reorder the terms: -13 + x = 11.789826123 Solving -13 + x = 11.789826123 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 = 11.789826123 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.789826123 + 13 x = 11.789826123 + 13 Combine like terms: 11.789826123 + 13 = 24.789826123 x = 24.789826123 Simplifying x = 24.789826123Subproblem 2
x + -13 = -11.789826123 Simplifying x + -13 = -11.789826123 Reorder the terms: -13 + x = -11.789826123 Solving -13 + x = -11.789826123 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 = -11.789826123 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.789826123 + 13 x = -11.789826123 + 13 Combine like terms: -11.789826123 + 13 = 1.210173877 x = 1.210173877 Simplifying x = 1.210173877Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.789826123, 1.210173877}
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