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Simplifying x + (2x + -12.5) + x(2x + -12.5) = 0 Reorder the terms: x + (-12.5 + 2x) + x(2x + -12.5) = 0 Remove parenthesis around (-12.5 + 2x) x + -12.5 + 2x + x(2x + -12.5) = 0 Reorder the terms: x + -12.5 + 2x + x(-12.5 + 2x) = 0 x + -12.5 + 2x + (-12.5 * x + 2x * x) = 0 x + -12.5 + 2x + (-12.5x + 2x2) = 0 Reorder the terms: -12.5 + x + 2x + -12.5x + 2x2 = 0 Combine like terms: x + 2x = 3x -12.5 + 3x + -12.5x + 2x2 = 0 Combine like terms: 3x + -12.5x = -9.5x -12.5 + -9.5x + 2x2 = 0 Solving -12.5 + -9.5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.25 + -4.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -4.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -4.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -4.75x + x2 = 0 + 6.25 -4.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -4.75x + x2 = 6.25 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 6.25 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 6.25 + 5.640625 Combine like terms: 6.25 + 5.640625 = 11.890625 5.640625 + -4.75x + x2 = 11.890625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (x + -2.375) equal to 3.448278556 and -3.448278556.Subproblem 1
x + -2.375 = 3.448278556 Simplifying x + -2.375 = 3.448278556 Reorder the terms: -2.375 + x = 3.448278556 Solving -2.375 + x = 3.448278556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 3.448278556 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.448278556 + 2.375 x = 3.448278556 + 2.375 Combine like terms: 3.448278556 + 2.375 = 5.823278556 x = 5.823278556 Simplifying x = 5.823278556Subproblem 2
x + -2.375 = -3.448278556 Simplifying x + -2.375 = -3.448278556 Reorder the terms: -2.375 + x = -3.448278556 Solving -2.375 + x = -3.448278556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -3.448278556 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.448278556 + 2.375 x = -3.448278556 + 2.375 Combine like terms: -3.448278556 + 2.375 = -1.073278556 x = -1.073278556 Simplifying x = -1.073278556Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.823278556, -1.073278556}
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