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Simplifying 0.25x2 + 6.5x + -117 = 0 Reorder the terms: -117 + 6.5x + 0.25x2 = 0 Solving -117 + 6.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -468 + 26x + x2 = 0 Move the constant term to the right: Add '468' to each side of the equation. -468 + 26x + 468 + x2 = 0 + 468 Reorder the terms: -468 + 468 + 26x + x2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + 26x + x2 = 0 + 468 26x + x2 = 0 + 468 Combine like terms: 0 + 468 = 468 26x + x2 = 468 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 = 468 + 169 Reorder the terms: 169 + 26x + x2 = 468 + 169 Combine like terms: 468 + 169 = 637 169 + 26x + x2 = 637 Factor a perfect square on the left side: (x + 13)(x + 13) = 637 Calculate the square root of the right side: 25.238858928 Break this problem into two subproblems by setting (x + 13) equal to 25.238858928 and -25.238858928.Subproblem 1
x + 13 = 25.238858928 Simplifying x + 13 = 25.238858928 Reorder the terms: 13 + x = 25.238858928 Solving 13 + x = 25.238858928 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 = 25.238858928 + -13 Combine like terms: 13 + -13 = 0 0 + x = 25.238858928 + -13 x = 25.238858928 + -13 Combine like terms: 25.238858928 + -13 = 12.238858928 x = 12.238858928 Simplifying x = 12.238858928Subproblem 2
x + 13 = -25.238858928 Simplifying x + 13 = -25.238858928 Reorder the terms: 13 + x = -25.238858928 Solving 13 + x = -25.238858928 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 = -25.238858928 + -13 Combine like terms: 13 + -13 = 0 0 + x = -25.238858928 + -13 x = -25.238858928 + -13 Combine like terms: -25.238858928 + -13 = -38.238858928 x = -38.238858928 Simplifying x = -38.238858928Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.238858928, -38.238858928}
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