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Simplifying (9x3 + -7x2 + 8x) + (2x3 + 9x2 + -12x) = 0 Reorder the terms: (8x + -7x2 + 9x3) + (2x3 + 9x2 + -12x) = 0 Remove parenthesis around (8x + -7x2 + 9x3) 8x + -7x2 + 9x3 + (2x3 + 9x2 + -12x) = 0 Reorder the terms: 8x + -7x2 + 9x3 + (-12x + 9x2 + 2x3) = 0 Remove parenthesis around (-12x + 9x2 + 2x3) 8x + -7x2 + 9x3 + -12x + 9x2 + 2x3 = 0 Reorder the terms: 8x + -12x + -7x2 + 9x2 + 9x3 + 2x3 = 0 Combine like terms: 8x + -12x = -4x -4x + -7x2 + 9x2 + 9x3 + 2x3 = 0 Combine like terms: -7x2 + 9x2 = 2x2 -4x + 2x2 + 9x3 + 2x3 = 0 Combine like terms: 9x3 + 2x3 = 11x3 -4x + 2x2 + 11x3 = 0 Solving -4x + 2x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 2x + 11x2) = 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 + 2x + 11x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + 11x2 = 0 Solving -4 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 0.1818181818x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 0.1818181818x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 0.1818181818x + x2 = 0 + 0.3636363636 0.1818181818x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 0.1818181818x + x2 = 0.3636363636 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 0.3636363636 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 0.3636363636 + 0.008264462808 Combine like terms: 0.3636363636 + 0.008264462808 = 0.371900826408 0.008264462808 + 0.1818181818x + x2 = 0.371900826408 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 0.371900826408 Calculate the square root of the right side: 0.609836721 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 0.609836721 and -0.609836721.Subproblem 1
x + 0.0909090909 = 0.609836721 Simplifying x + 0.0909090909 = 0.609836721 Reorder the terms: 0.0909090909 + x = 0.609836721 Solving 0.0909090909 + x = 0.609836721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 0.609836721 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.609836721 + -0.0909090909 x = 0.609836721 + -0.0909090909 Combine like terms: 0.609836721 + -0.0909090909 = 0.5189276301 x = 0.5189276301 Simplifying x = 0.5189276301Subproblem 2
x + 0.0909090909 = -0.609836721 Simplifying x + 0.0909090909 = -0.609836721 Reorder the terms: 0.0909090909 + x = -0.609836721 Solving 0.0909090909 + x = -0.609836721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -0.609836721 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.609836721 + -0.0909090909 x = -0.609836721 + -0.0909090909 Combine like terms: -0.609836721 + -0.0909090909 = -0.7007458119 x = -0.7007458119 Simplifying x = -0.7007458119Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5189276301, -0.7007458119}Solution
x = {0, 0.5189276301, -0.7007458119}
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