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Simplifying x(x * x + 2x + -1) + -4x(-2x + 3) = 0 Multiply x * x x(x2 + 2x + -1) + -4x(-2x + 3) = 0 Reorder the terms: x(-1 + 2x + x2) + -4x(-2x + 3) = 0 (-1 * x + 2x * x + x2 * x) + -4x(-2x + 3) = 0 (-1x + 2x2 + x3) + -4x(-2x + 3) = 0 Reorder the terms: -1x + 2x2 + x3 + -4x(3 + -2x) = 0 -1x + 2x2 + x3 + (3 * -4x + -2x * -4x) = 0 -1x + 2x2 + x3 + (-12x + 8x2) = 0 Reorder the terms: -1x + -12x + 2x2 + 8x2 + x3 = 0 Combine like terms: -1x + -12x = -13x -13x + 2x2 + 8x2 + x3 = 0 Combine like terms: 2x2 + 8x2 = 10x2 -13x + 10x2 + x3 = 0 Solving -13x + 10x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + 10x + x2) = 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 '(-13 + 10x + x2)' equal to zero and attempt to solve: Simplifying -13 + 10x + x2 = 0 Solving -13 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 10x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 10x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 10x + x2 = 0 + 13 10x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 10x + x2 = 13 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 13 + 25 Reorder the terms: 25 + 10x + x2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + 10x + x2 = 38 Factor a perfect square on the left side: (x + 5)(x + 5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 5) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 5 = 6.164414003 Simplifying x + 5 = 6.164414003 Reorder the terms: 5 + x = 6.164414003 Solving 5 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.164414003 + -5 x = 6.164414003 + -5 Combine like terms: 6.164414003 + -5 = 1.164414003 x = 1.164414003 Simplifying x = 1.164414003Subproblem 2
x + 5 = -6.164414003 Simplifying x + 5 = -6.164414003 Reorder the terms: 5 + x = -6.164414003 Solving 5 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.164414003 + -5 x = -6.164414003 + -5 Combine like terms: -6.164414003 + -5 = -11.164414003 x = -11.164414003 Simplifying x = -11.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.164414003, -11.164414003}Solution
x = {0, 1.164414003, -11.164414003}
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