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Simplifying x = 4x2 + 42x + -50 Reorder the terms: x = -50 + 42x + 4x2 Solving x = -50 + 42x + 4x2 Solving for variable 'x'. Reorder the terms: 50 + x + -42x + -4x2 = -50 + 42x + 4x2 + 50 + -42x + -4x2 Combine like terms: x + -42x = -41x 50 + -41x + -4x2 = -50 + 42x + 4x2 + 50 + -42x + -4x2 Reorder the terms: 50 + -41x + -4x2 = -50 + 50 + 42x + -42x + 4x2 + -4x2 Combine like terms: -50 + 50 = 0 50 + -41x + -4x2 = 0 + 42x + -42x + 4x2 + -4x2 50 + -41x + -4x2 = 42x + -42x + 4x2 + -4x2 Combine like terms: 42x + -42x = 0 50 + -41x + -4x2 = 0 + 4x2 + -4x2 50 + -41x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 50 + -41x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.5 + 10.25x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 10.25x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 10.25x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 10.25x + x2 = 0 + 12.5 10.25x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 10.25x + x2 = 12.5 The x term is 10.25x. Take half its coefficient (5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. 10.25x + 26.265625 + x2 = 12.5 + 26.265625 Reorder the terms: 26.265625 + 10.25x + x2 = 12.5 + 26.265625 Combine like terms: 12.5 + 26.265625 = 38.765625 26.265625 + 10.25x + x2 = 38.765625 Factor a perfect square on the left side: (x + 5.125)(x + 5.125) = 38.765625 Calculate the square root of the right side: 6.226204703 Break this problem into two subproblems by setting (x + 5.125) equal to 6.226204703 and -6.226204703.Subproblem 1
x + 5.125 = 6.226204703 Simplifying x + 5.125 = 6.226204703 Reorder the terms: 5.125 + x = 6.226204703 Solving 5.125 + x = 6.226204703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = 6.226204703 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = 6.226204703 + -5.125 x = 6.226204703 + -5.125 Combine like terms: 6.226204703 + -5.125 = 1.101204703 x = 1.101204703 Simplifying x = 1.101204703Subproblem 2
x + 5.125 = -6.226204703 Simplifying x + 5.125 = -6.226204703 Reorder the terms: 5.125 + x = -6.226204703 Solving 5.125 + x = -6.226204703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = -6.226204703 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = -6.226204703 + -5.125 x = -6.226204703 + -5.125 Combine like terms: -6.226204703 + -5.125 = -11.351204703 x = -11.351204703 Simplifying x = -11.351204703Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.101204703, -11.351204703}
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