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Simplifying 3x + -1x2 = x3 + 2x2 + -4x Reorder the terms: 3x + -1x2 = -4x + 2x2 + x3 Solving 3x + -1x2 = -4x + 2x2 + x3 Solving for variable 'x'. Reorder the terms: 3x + 4x + -1x2 + -2x2 + -1x3 = -4x + 2x2 + x3 + 4x + -2x2 + -1x3 Combine like terms: 3x + 4x = 7x 7x + -1x2 + -2x2 + -1x3 = -4x + 2x2 + x3 + 4x + -2x2 + -1x3 Combine like terms: -1x2 + -2x2 = -3x2 7x + -3x2 + -1x3 = -4x + 2x2 + x3 + 4x + -2x2 + -1x3 Reorder the terms: 7x + -3x2 + -1x3 = -4x + 4x + 2x2 + -2x2 + x3 + -1x3 Combine like terms: -4x + 4x = 0 7x + -3x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3 7x + -3x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3 Combine like terms: 2x2 + -2x2 = 0 7x + -3x2 + -1x3 = 0 + x3 + -1x3 7x + -3x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 7x + -3x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(7 + -3x + -1x2) = 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 '(7 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 7 + -3x + -1x2 = 0 Solving 7 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 3x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 3x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x + x2 = 0 + 7 3x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3x + x2 = 7 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 7 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + 3x + x2 = 9.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + 1.5 = 3.041381265 Simplifying x + 1.5 = 3.041381265 Reorder the terms: 1.5 + x = 3.041381265 Solving 1.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.041381265 + -1.5 x = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 x = 1.541381265 Simplifying x = 1.541381265Subproblem 2
x + 1.5 = -3.041381265 Simplifying x + 1.5 = -3.041381265 Reorder the terms: 1.5 + x = -3.041381265 Solving 1.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.041381265 + -1.5 x = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 x = -4.541381265 Simplifying x = -4.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.541381265, -4.541381265}Solution
x = {0, 1.541381265, -4.541381265}
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