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Simplifying x((x + -5)(x2 + -3x) + 9x) + -10x2 = 0 Reorder the terms: x((-5 + x)(x2 + -3x) + 9x) + -10x2 = 0 Reorder the terms: x((-5 + x)(-3x + x2) + 9x) + -10x2 = 0 Multiply (-5 + x) * (-3x + x2) x((-5(-3x + x2) + x(-3x + x2)) + 9x) + -10x2 = 0 x(((-3x * -5 + x2 * -5) + x(-3x + x2)) + 9x) + -10x2 = 0 x(((15x + -5x2) + x(-3x + x2)) + 9x) + -10x2 = 0 x((15x + -5x2 + (-3x * x + x2 * x)) + 9x) + -10x2 = 0 x((15x + -5x2 + (-3x2 + x3)) + 9x) + -10x2 = 0 Combine like terms: -5x2 + -3x2 = -8x2 x((15x + -8x2 + x3) + 9x) + -10x2 = 0 Reorder the terms: x(15x + 9x + -8x2 + x3) + -10x2 = 0 Combine like terms: 15x + 9x = 24x x(24x + -8x2 + x3) + -10x2 = 0 (24x * x + -8x2 * x + x3 * x) + -10x2 = 0 (24x2 + -8x3 + x4) + -10x2 = 0 Reorder the terms: 24x2 + -10x2 + -8x3 + x4 = 0 Combine like terms: 24x2 + -10x2 = 14x2 14x2 + -8x3 + x4 = 0 Solving 14x2 + -8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(14 + -8x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(14 + -8x + x2)' equal to zero and attempt to solve: Simplifying 14 + -8x + x2 = 0 Solving 14 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8x + x2 = 0 + -14 -8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8x + x2 = -14 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -14 + 16 Reorder the terms: 16 + -8x + x2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8x + x2 = 2 Factor a perfect square on the left side: (x + -4)(x + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -4 = 1.414213562 Simplifying x + -4 = 1.414213562 Reorder the terms: -4 + x = 1.414213562 Solving -4 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.414213562 + 4 x = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 x = 5.414213562 Simplifying x = 5.414213562Subproblem 2
x + -4 = -1.414213562 Simplifying x + -4 = -1.414213562 Reorder the terms: -4 + x = -1.414213562 Solving -4 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.414213562 + 4 x = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 x = 2.585786438 Simplifying x = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.414213562, 2.585786438}Solution
x = {0, 5.414213562, 2.585786438}
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