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Simplifying x2 + 3x2 + -25x + -75 = 0 Reorder the terms: -75 + -25x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 -75 + -25x + 4x2 = 0 Solving -75 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -6.25x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -6.25x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -6.25x + x2 = 0 + 18.75 -6.25x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -6.25x + x2 = 18.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 18.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 18.75 + 9.765625 Combine like terms: 18.75 + 9.765625 = 28.515625 9.765625 + -6.25x + x2 = 28.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 28.515625 Calculate the square root of the right side: 5.340002341 Break this problem into two subproblems by setting (x + -3.125) equal to 5.340002341 and -5.340002341.Subproblem 1
x + -3.125 = 5.340002341 Simplifying x + -3.125 = 5.340002341 Reorder the terms: -3.125 + x = 5.340002341 Solving -3.125 + x = 5.340002341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 5.340002341 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 5.340002341 + 3.125 x = 5.340002341 + 3.125 Combine like terms: 5.340002341 + 3.125 = 8.465002341 x = 8.465002341 Simplifying x = 8.465002341Subproblem 2
x + -3.125 = -5.340002341 Simplifying x + -3.125 = -5.340002341 Reorder the terms: -3.125 + x = -5.340002341 Solving -3.125 + x = -5.340002341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -5.340002341 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -5.340002341 + 3.125 x = -5.340002341 + 3.125 Combine like terms: -5.340002341 + 3.125 = -2.215002341 x = -2.215002341 Simplifying x = -2.215002341Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.465002341, -2.215002341}
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