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Simplifying (2x3 + -4x2 + 6x) + (7x3 + 9x2 + -12x) = 0 Reorder the terms: (6x + -4x2 + 2x3) + (7x3 + 9x2 + -12x) = 0 Remove parenthesis around (6x + -4x2 + 2x3) 6x + -4x2 + 2x3 + (7x3 + 9x2 + -12x) = 0 Reorder the terms: 6x + -4x2 + 2x3 + (-12x + 9x2 + 7x3) = 0 Remove parenthesis around (-12x + 9x2 + 7x3) 6x + -4x2 + 2x3 + -12x + 9x2 + 7x3 = 0 Reorder the terms: 6x + -12x + -4x2 + 9x2 + 2x3 + 7x3 = 0 Combine like terms: 6x + -12x = -6x -6x + -4x2 + 9x2 + 2x3 + 7x3 = 0 Combine like terms: -4x2 + 9x2 = 5x2 -6x + 5x2 + 2x3 + 7x3 = 0 Combine like terms: 2x3 + 7x3 = 9x3 -6x + 5x2 + 9x3 = 0 Solving -6x + 5x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 5x + 9x2) = 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 '(-6 + 5x + 9x2)' equal to zero and attempt to solve: Simplifying -6 + 5x + 9x2 = 0 Solving -6 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.5555555556x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.5555555556x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.6666666667 0.5555555556x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.5555555556x + x2 = 0.6666666667 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.6666666667 + 0.07716049384 Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054 0.07716049384 + 0.5555555556x + x2 = 0.74382716054 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.74382716054 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.86245415 and -0.86245415.Subproblem 1
x + 0.2777777778 = 0.86245415 Simplifying x + 0.2777777778 = 0.86245415 Reorder the terms: 0.2777777778 + x = 0.86245415 Solving 0.2777777778 + x = 0.86245415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.86245415 + -0.2777777778 x = 0.86245415 + -0.2777777778 Combine like terms: 0.86245415 + -0.2777777778 = 0.5846763722 x = 0.5846763722 Simplifying x = 0.5846763722Subproblem 2
x + 0.2777777778 = -0.86245415 Simplifying x + 0.2777777778 = -0.86245415 Reorder the terms: 0.2777777778 + x = -0.86245415 Solving 0.2777777778 + x = -0.86245415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.86245415 + -0.2777777778 x = -0.86245415 + -0.2777777778 Combine like terms: -0.86245415 + -0.2777777778 = -1.1402319278 x = -1.1402319278 Simplifying x = -1.1402319278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5846763722, -1.1402319278}Solution
x = {0, 0.5846763722, -1.1402319278}
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