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Simplifying 4x3 + 25x2 + -56x = x Reorder the terms: -56x + 25x2 + 4x3 = x Solving -56x + 25x2 + 4x3 = x Solving for variable 'x'. Reorder the terms: -56x + -1x + 25x2 + 4x3 = x + -1x Combine like terms: -56x + -1x = -57x -57x + 25x2 + 4x3 = x + -1x Combine like terms: x + -1x = 0 -57x + 25x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-57 + 25x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-57 + 25x + 4x2)' equal to zero and attempt to solve: Simplifying -57 + 25x + 4x2 = 0 Solving -57 + 25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14.25 + 6.25x + x2 = 0 Move the constant term to the right: Add '14.25' to each side of the equation. -14.25 + 6.25x + 14.25 + x2 = 0 + 14.25 Reorder the terms: -14.25 + 14.25 + 6.25x + x2 = 0 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + 6.25x + x2 = 0 + 14.25 6.25x + x2 = 0 + 14.25 Combine like terms: 0 + 14.25 = 14.25 6.25x + x2 = 14.25 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 = 14.25 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 14.25 + 9.765625 Combine like terms: 14.25 + 9.765625 = 24.015625 9.765625 + 6.25x + x2 = 24.015625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 24.015625 Calculate the square root of the right side: 4.900573946 Break this problem into two subproblems by setting (x + 3.125) equal to 4.900573946 and -4.900573946.Subproblem 1
x + 3.125 = 4.900573946 Simplifying x + 3.125 = 4.900573946 Reorder the terms: 3.125 + x = 4.900573946 Solving 3.125 + x = 4.900573946 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 = 4.900573946 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 4.900573946 + -3.125 x = 4.900573946 + -3.125 Combine like terms: 4.900573946 + -3.125 = 1.775573946 x = 1.775573946 Simplifying x = 1.775573946Subproblem 2
x + 3.125 = -4.900573946 Simplifying x + 3.125 = -4.900573946 Reorder the terms: 3.125 + x = -4.900573946 Solving 3.125 + x = -4.900573946 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 = -4.900573946 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -4.900573946 + -3.125 x = -4.900573946 + -3.125 Combine like terms: -4.900573946 + -3.125 = -8.025573946 x = -8.025573946 Simplifying x = -8.025573946Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.775573946, -8.025573946}Solution
x = {0, 1.775573946, -8.025573946}
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