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Simplifying 2x(3x2 + -7x + 8) = 0 Reorder the terms: 2x(8 + -7x + 3x2) = 0 (8 * 2x + -7x * 2x + 3x2 * 2x) = 0 (16x + -14x2 + 6x3) = 0 Solving 16x + -14x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(8 + -7x + 3x2) = 0 Ignore the factor 2.Subproblem 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 '(8 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + -7x + 3x2 = 0 Solving 8 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -2.333333333x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -2.333333333x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + -2.666666667 -2.333333333x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -2.333333333x + x2 = -2.666666667 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -2.666666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -2.666666667 + 1.361111112 Combine like terms: -2.666666667 + 1.361111112 = -1.305555555 1.361111112 + -2.333333333x + x2 = -1.305555555 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = -1.305555555 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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