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Simplifying 15x4 + 9x3 + 24x2 = 0 Reorder the terms: 24x2 + 9x3 + 15x4 = 0 Solving 24x2 + 9x3 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(8 + 3x + 5x2) = 0 Ignore the factor 3.Subproblem 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 '(8 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying 8 + 3x + 5x2 = 0 Solving 8 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + 0.6x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 0.6x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 0.6x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 0.6x + x2 = 0 + -1.6 0.6x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 0.6x + x2 = -1.6 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -1.6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -1.6 + 0.09 Combine like terms: -1.6 + 0.09 = -1.51 0.09 + 0.6x + x2 = -1.51 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -1.51 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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