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Simplifying (3x7 + -3x4 + 8x) + (6x7 + -5x4 + 7x) = 0 Reorder the terms: (8x + -3x4 + 3x7) + (6x7 + -5x4 + 7x) = 0 Remove parenthesis around (8x + -3x4 + 3x7) 8x + -3x4 + 3x7 + (6x7 + -5x4 + 7x) = 0 Reorder the terms: 8x + -3x4 + 3x7 + (7x + -5x4 + 6x7) = 0 Remove parenthesis around (7x + -5x4 + 6x7) 8x + -3x4 + 3x7 + 7x + -5x4 + 6x7 = 0 Reorder the terms: 8x + 7x + -3x4 + -5x4 + 3x7 + 6x7 = 0 Combine like terms: 8x + 7x = 15x 15x + -3x4 + -5x4 + 3x7 + 6x7 = 0 Combine like terms: -3x4 + -5x4 = -8x4 15x + -8x4 + 3x7 + 6x7 = 0 Combine like terms: 3x7 + 6x7 = 9x7 15x + -8x4 + 9x7 = 0 Solving 15x + -8x4 + 9x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + -8x3 + 9x6) = 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 '(15 + -8x3 + 9x6)' equal to zero and attempt to solve: Simplifying 15 + -8x3 + 9x6 = 0 Solving 15 + -8x3 + 9x6 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.666666667 + -0.8888888889x3 + x6 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -0.8888888889x3 + -1.666666667 + x6 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -0.8888888889x3 + x6 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -0.8888888889x3 + x6 = 0 + -1.666666667 -0.8888888889x3 + x6 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -0.8888888889x3 + x6 = -1.666666667 The x term is -0.8888888889x3. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x3 + 0.1975308642 + x6 = -1.666666667 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x3 + x6 = -1.666666667 + 0.1975308642 Combine like terms: -1.666666667 + 0.1975308642 = -1.4691358028 0.1975308642 + -0.8888888889x3 + x6 = -1.4691358028 Factor a perfect square on the left side: (x3 + -0.4444444445)(x3 + -0.4444444445) = -1.4691358028 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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