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Simplifying (4x4 + -7x3 + 9x2) + -1(2x4 + 1x3 + -6x2) = 0 Reorder the terms: (9x2 + -7x3 + 4x4) + -1(2x4 + 1x3 + -6x2) = 0 Remove parenthesis around (9x2 + -7x3 + 4x4) 9x2 + -7x3 + 4x4 + -1(2x4 + 1x3 + -6x2) = 0 Reorder the terms: 9x2 + -7x3 + 4x4 + -1(-6x2 + 1x3 + 2x4) = 0 9x2 + -7x3 + 4x4 + (-6x2 * -1 + 1x3 * -1 + 2x4 * -1) = 0 9x2 + -7x3 + 4x4 + (6x2 + -1x3 + -2x4) = 0 Reorder the terms: 9x2 + 6x2 + -7x3 + -1x3 + 4x4 + -2x4 = 0 Combine like terms: 9x2 + 6x2 = 15x2 15x2 + -7x3 + -1x3 + 4x4 + -2x4 = 0 Combine like terms: -7x3 + -1x3 = -8x3 15x2 + -8x3 + 4x4 + -2x4 = 0 Combine like terms: 4x4 + -2x4 = 2x4 15x2 + -8x3 + 2x4 = 0 Solving 15x2 + -8x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(15 + -8x + 2x2) = 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 '(15 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -8x + 2x2 = 0 Solving 15 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -4x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -4x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -4x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -4x + x2 = 0 + -7.5 -4x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -4x + x2 = -7.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -7.5 + 4 Reorder the terms: 4 + -4x + x2 = -7.5 + 4 Combine like terms: -7.5 + 4 = -3.5 4 + -4x + x2 = -3.5 Factor a perfect square on the left side: (x + -2)(x + -2) = -3.5 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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