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Simplifying 3x3 + -5x2 + 9x + -5 = 5x3 + 8x2 + 10x + -5 Reorder the terms: -5 + 9x + -5x2 + 3x3 = 5x3 + 8x2 + 10x + -5 Reorder the terms: -5 + 9x + -5x2 + 3x3 = -5 + 10x + 8x2 + 5x3 Add '5' to each side of the equation. -5 + 9x + -5x2 + 5 + 3x3 = -5 + 10x + 8x2 + 5 + 5x3 Reorder the terms: -5 + 5 + 9x + -5x2 + 3x3 = -5 + 10x + 8x2 + 5 + 5x3 Combine like terms: -5 + 5 = 0 0 + 9x + -5x2 + 3x3 = -5 + 10x + 8x2 + 5 + 5x3 9x + -5x2 + 3x3 = -5 + 10x + 8x2 + 5 + 5x3 Reorder the terms: 9x + -5x2 + 3x3 = -5 + 5 + 10x + 8x2 + 5x3 Combine like terms: -5 + 5 = 0 9x + -5x2 + 3x3 = 0 + 10x + 8x2 + 5x3 9x + -5x2 + 3x3 = 10x + 8x2 + 5x3 Solving 9x + -5x2 + 3x3 = 10x + 8x2 + 5x3 Solving for variable 'x'. Reorder the terms: 9x + -10x + -5x2 + -8x2 + 3x3 + -5x3 = 10x + 8x2 + 5x3 + -10x + -8x2 + -5x3 Combine like terms: 9x + -10x = -1x -1x + -5x2 + -8x2 + 3x3 + -5x3 = 10x + 8x2 + 5x3 + -10x + -8x2 + -5x3 Combine like terms: -5x2 + -8x2 = -13x2 -1x + -13x2 + 3x3 + -5x3 = 10x + 8x2 + 5x3 + -10x + -8x2 + -5x3 Combine like terms: 3x3 + -5x3 = -2x3 -1x + -13x2 + -2x3 = 10x + 8x2 + 5x3 + -10x + -8x2 + -5x3 Reorder the terms: -1x + -13x2 + -2x3 = 10x + -10x + 8x2 + -8x2 + 5x3 + -5x3 Combine like terms: 10x + -10x = 0 -1x + -13x2 + -2x3 = 0 + 8x2 + -8x2 + 5x3 + -5x3 -1x + -13x2 + -2x3 = 8x2 + -8x2 + 5x3 + -5x3 Combine like terms: 8x2 + -8x2 = 0 -1x + -13x2 + -2x3 = 0 + 5x3 + -5x3 -1x + -13x2 + -2x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -1x + -13x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(1 + 13x + 2x2) = 0 Ignore the factor -1.Subproblem 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 '(1 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 13x + 2x2 = 0 Solving 1 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 6.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 6.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 6.5x + x2 = 0 + -0.5 6.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 6.5x + x2 = -0.5 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -0.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -0.5 + 10.5625 Combine like terms: -0.5 + 10.5625 = 10.0625 10.5625 + 6.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 3.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 3.25 = 3.172144385 Simplifying x + 3.25 = 3.172144385 Reorder the terms: 3.25 + x = 3.172144385 Solving 3.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.172144385 + -3.25 x = 3.172144385 + -3.25 Combine like terms: 3.172144385 + -3.25 = -0.077855615 x = -0.077855615 Simplifying x = -0.077855615Subproblem 2
x + 3.25 = -3.172144385 Simplifying x + 3.25 = -3.172144385 Reorder the terms: 3.25 + x = -3.172144385 Solving 3.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.172144385 + -3.25 x = -3.172144385 + -3.25 Combine like terms: -3.172144385 + -3.25 = -6.422144385 x = -6.422144385 Simplifying x = -6.422144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.077855615, -6.422144385}Solution
x = {0, -0.077855615, -6.422144385}
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