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Simplifying 19264 = 116x2 + 705x Reorder the terms: 19264 = 705x + 116x2 Solving 19264 = 705x + 116x2 Solving for variable 'x'. Reorder the terms: 19264 + -705x + -116x2 = 705x + -705x + 116x2 + -116x2 Combine like terms: 705x + -705x = 0 19264 + -705x + -116x2 = 0 + 116x2 + -116x2 19264 + -705x + -116x2 = 116x2 + -116x2 Combine like terms: 116x2 + -116x2 = 0 19264 + -705x + -116x2 = 0 Begin completing the square. Divide all terms by -116 the coefficient of the squared term: Divide each side by '-116'. -166.0689655 + 6.077586207x + x2 = 0 Move the constant term to the right: Add '166.0689655' to each side of the equation. -166.0689655 + 6.077586207x + 166.0689655 + x2 = 0 + 166.0689655 Reorder the terms: -166.0689655 + 166.0689655 + 6.077586207x + x2 = 0 + 166.0689655 Combine like terms: -166.0689655 + 166.0689655 = 0.0000000 0.0000000 + 6.077586207x + x2 = 0 + 166.0689655 6.077586207x + x2 = 0 + 166.0689655 Combine like terms: 0 + 166.0689655 = 166.0689655 6.077586207x + x2 = 166.0689655 The x term is 6.077586207x. Take half its coefficient (3.038793104). Square it (9.234263529) and add it to both sides. Add '9.234263529' to each side of the equation. 6.077586207x + 9.234263529 + x2 = 166.0689655 + 9.234263529 Reorder the terms: 9.234263529 + 6.077586207x + x2 = 166.0689655 + 9.234263529 Combine like terms: 166.0689655 + 9.234263529 = 175.303229029 9.234263529 + 6.077586207x + x2 = 175.303229029 Factor a perfect square on the left side: (x + 3.038793104)(x + 3.038793104) = 175.303229029 Calculate the square root of the right side: 13.240212575 Break this problem into two subproblems by setting (x + 3.038793104) equal to 13.240212575 and -13.240212575.Subproblem 1
x + 3.038793104 = 13.240212575 Simplifying x + 3.038793104 = 13.240212575 Reorder the terms: 3.038793104 + x = 13.240212575 Solving 3.038793104 + x = 13.240212575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.038793104' to each side of the equation. 3.038793104 + -3.038793104 + x = 13.240212575 + -3.038793104 Combine like terms: 3.038793104 + -3.038793104 = 0.000000000 0.000000000 + x = 13.240212575 + -3.038793104 x = 13.240212575 + -3.038793104 Combine like terms: 13.240212575 + -3.038793104 = 10.201419471 x = 10.201419471 Simplifying x = 10.201419471Subproblem 2
x + 3.038793104 = -13.240212575 Simplifying x + 3.038793104 = -13.240212575 Reorder the terms: 3.038793104 + x = -13.240212575 Solving 3.038793104 + x = -13.240212575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.038793104' to each side of the equation. 3.038793104 + -3.038793104 + x = -13.240212575 + -3.038793104 Combine like terms: 3.038793104 + -3.038793104 = 0.000000000 0.000000000 + x = -13.240212575 + -3.038793104 x = -13.240212575 + -3.038793104 Combine like terms: -13.240212575 + -3.038793104 = -16.279005679 x = -16.279005679 Simplifying x = -16.279005679Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.201419471, -16.279005679}
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