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Simplifying (10x3 + 6x2 + 4x) + -1(8x3 + 2x2 + -3x) = 0 Reorder the terms: (4x + 6x2 + 10x3) + -1(8x3 + 2x2 + -3x) = 0 Remove parenthesis around (4x + 6x2 + 10x3) 4x + 6x2 + 10x3 + -1(8x3 + 2x2 + -3x) = 0 Reorder the terms: 4x + 6x2 + 10x3 + -1(-3x + 2x2 + 8x3) = 0 4x + 6x2 + 10x3 + (-3x * -1 + 2x2 * -1 + 8x3 * -1) = 0 4x + 6x2 + 10x3 + (3x + -2x2 + -8x3) = 0 Reorder the terms: 4x + 3x + 6x2 + -2x2 + 10x3 + -8x3 = 0 Combine like terms: 4x + 3x = 7x 7x + 6x2 + -2x2 + 10x3 + -8x3 = 0 Combine like terms: 6x2 + -2x2 = 4x2 7x + 4x2 + 10x3 + -8x3 = 0 Combine like terms: 10x3 + -8x3 = 2x3 7x + 4x2 + 2x3 = 0 Solving 7x + 4x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 4x + 2x2) = 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 '(7 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 2x2 = 0 Solving 7 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 2x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 2x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 2x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 2x + x2 = 0 + -3.5 2x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 2x + x2 = -3.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -3.5 + 1 Reorder the terms: 1 + 2x + x2 = -3.5 + 1 Combine like terms: -3.5 + 1 = -2.5 1 + 2x + x2 = -2.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -2.5 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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