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Simplifying 0 = 200x2 + 8600x + -89408 Reorder the terms: 0 = -89408 + 8600x + 200x2 Solving 0 = -89408 + 8600x + 200x2 Solving for variable 'x'. Combine like terms: 0 + 89408 = 89408 89408 + -8600x + -200x2 = -89408 + 8600x + 200x2 + 89408 + -8600x + -200x2 Reorder the terms: 89408 + -8600x + -200x2 = -89408 + 89408 + 8600x + -8600x + 200x2 + -200x2 Combine like terms: -89408 + 89408 = 0 89408 + -8600x + -200x2 = 0 + 8600x + -8600x + 200x2 + -200x2 89408 + -8600x + -200x2 = 8600x + -8600x + 200x2 + -200x2 Combine like terms: 8600x + -8600x = 0 89408 + -8600x + -200x2 = 0 + 200x2 + -200x2 89408 + -8600x + -200x2 = 200x2 + -200x2 Combine like terms: 200x2 + -200x2 = 0 89408 + -8600x + -200x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(11176 + -1075x + -25x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(11176 + -1075x + -25x2)' equal to zero and attempt to solve: Simplifying 11176 + -1075x + -25x2 = 0 Solving 11176 + -1075x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -447.04 + 43x + x2 = 0 Move the constant term to the right: Add '447.04' to each side of the equation. -447.04 + 43x + 447.04 + x2 = 0 + 447.04 Reorder the terms: -447.04 + 447.04 + 43x + x2 = 0 + 447.04 Combine like terms: -447.04 + 447.04 = 0.00 0.00 + 43x + x2 = 0 + 447.04 43x + x2 = 0 + 447.04 Combine like terms: 0 + 447.04 = 447.04 43x + x2 = 447.04 The x term is 43x. Take half its coefficient (21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. 43x + 462.25 + x2 = 447.04 + 462.25 Reorder the terms: 462.25 + 43x + x2 = 447.04 + 462.25 Combine like terms: 447.04 + 462.25 = 909.29 462.25 + 43x + x2 = 909.29 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 909.29 Calculate the square root of the right side: 30.154435826 Break this problem into two subproblems by setting (x + 21.5) equal to 30.154435826 and -30.154435826.Subproblem 1
x + 21.5 = 30.154435826 Simplifying x + 21.5 = 30.154435826 Reorder the terms: 21.5 + x = 30.154435826 Solving 21.5 + x = 30.154435826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 30.154435826 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 30.154435826 + -21.5 x = 30.154435826 + -21.5 Combine like terms: 30.154435826 + -21.5 = 8.654435826 x = 8.654435826 Simplifying x = 8.654435826Subproblem 2
x + 21.5 = -30.154435826 Simplifying x + 21.5 = -30.154435826 Reorder the terms: 21.5 + x = -30.154435826 Solving 21.5 + x = -30.154435826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -30.154435826 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -30.154435826 + -21.5 x = -30.154435826 + -21.5 Combine like terms: -30.154435826 + -21.5 = -51.654435826 x = -51.654435826 Simplifying x = -51.654435826Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.654435826, -51.654435826}Solution
x = {8.654435826, -51.654435826}
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