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Simplifying 4x(3x2 + 7) = 24x2 Reorder the terms: 4x(7 + 3x2) = 24x2 (7 * 4x + 3x2 * 4x) = 24x2 (28x + 12x3) = 24x2 Solving 28x + 12x3 = 24x2 Solving for variable 'x'. Reorder the terms: 28x + -24x2 + 12x3 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 28x + -24x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(7 + -6x + 3x2) = 0 Ignore the factor 4.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 '(7 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -6x + 3x2 = 0 Solving 7 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -2x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -2x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + -2.333333333 -2x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -2x + x2 = -2.333333333 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 = -2.333333333 + 1 Reorder the terms: 1 + -2x + x2 = -2.333333333 + 1 Combine like terms: -2.333333333 + 1 = -1.333333333 1 + -2x + x2 = -1.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = -1.333333333 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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