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Simplifying 0 = 2x3 + 5x2 + -4x Reorder the terms: 0 = -4x + 5x2 + 2x3 Solving 0 = -4x + 5x2 + 2x3 Solving for variable 'x'. Remove the zero: 4x + -5x2 + -2x3 = -4x + 5x2 + 2x3 + 4x + -5x2 + -2x3 Reorder the terms: 4x + -5x2 + -2x3 = -4x + 4x + 5x2 + -5x2 + 2x3 + -2x3 Combine like terms: -4x + 4x = 0 4x + -5x2 + -2x3 = 0 + 5x2 + -5x2 + 2x3 + -2x3 4x + -5x2 + -2x3 = 5x2 + -5x2 + 2x3 + -2x3 Combine like terms: 5x2 + -5x2 = 0 4x + -5x2 + -2x3 = 0 + 2x3 + -2x3 4x + -5x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 4x + -5x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -5x + -2x2) = 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 '(4 + -5x + -2x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + -2x2 = 0 Solving 4 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + 2.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.5x + x2 = 0 + 2 2.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.5x + x2 = 2 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 2 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + 2.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 1.25 = 1.887458609 Simplifying x + 1.25 = 1.887458609 Reorder the terms: 1.25 + x = 1.887458609 Solving 1.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.887458609 + -1.25 x = 1.887458609 + -1.25 Combine like terms: 1.887458609 + -1.25 = 0.637458609 x = 0.637458609 Simplifying x = 0.637458609Subproblem 2
x + 1.25 = -1.887458609 Simplifying x + 1.25 = -1.887458609 Reorder the terms: 1.25 + x = -1.887458609 Solving 1.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.887458609 + -1.25 x = -1.887458609 + -1.25 Combine like terms: -1.887458609 + -1.25 = -3.137458609 x = -3.137458609 Simplifying x = -3.137458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.637458609, -3.137458609}Solution
x = {0, 0.637458609, -3.137458609}
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