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Simplifying 45x4 + -24x3 + 48x2 = 0 Reorder the terms: 48x2 + -24x3 + 45x4 = 0 Solving 48x2 + -24x3 + 45x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(16 + -8x + 15x2) = 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 '(16 + -8x + 15x2)' equal to zero and attempt to solve: Simplifying 16 + -8x + 15x2 = 0 Solving 16 + -8x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.066666667 + -0.5333333333x + x2 = 0 Move the constant term to the right: Add '-1.066666667' to each side of the equation. 1.066666667 + -0.5333333333x + -1.066666667 + x2 = 0 + -1.066666667 Reorder the terms: 1.066666667 + -1.066666667 + -0.5333333333x + x2 = 0 + -1.066666667 Combine like terms: 1.066666667 + -1.066666667 = 0.000000000 0.000000000 + -0.5333333333x + x2 = 0 + -1.066666667 -0.5333333333x + x2 = 0 + -1.066666667 Combine like terms: 0 + -1.066666667 = -1.066666667 -0.5333333333x + x2 = -1.066666667 The x term is -0.5333333333x. Take half its coefficient (-0.2666666667). Square it (0.07111111113) and add it to both sides. Add '0.07111111113' to each side of the equation. -0.5333333333x + 0.07111111113 + x2 = -1.066666667 + 0.07111111113 Reorder the terms: 0.07111111113 + -0.5333333333x + x2 = -1.066666667 + 0.07111111113 Combine like terms: -1.066666667 + 0.07111111113 = -0.99555555587 0.07111111113 + -0.5333333333x + x2 = -0.99555555587 Factor a perfect square on the left side: (x + -0.2666666667)(x + -0.2666666667) = -0.99555555587 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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