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Simplifying 0 = 900x + -150x2 + 4x3 Solving 0 = 900x + -150x2 + 4x3 Solving for variable 'x'. Remove the zero: -900x + 150x2 + -4x3 = 900x + -150x2 + 4x3 + -900x + 150x2 + -4x3 Reorder the terms: -900x + 150x2 + -4x3 = 900x + -900x + -150x2 + 150x2 + 4x3 + -4x3 Combine like terms: 900x + -900x = 0 -900x + 150x2 + -4x3 = 0 + -150x2 + 150x2 + 4x3 + -4x3 -900x + 150x2 + -4x3 = -150x2 + 150x2 + 4x3 + -4x3 Combine like terms: -150x2 + 150x2 = 0 -900x + 150x2 + -4x3 = 0 + 4x3 + -4x3 -900x + 150x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -900x + 150x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-450 + 75x + -2x2) = 0 Factor a trinomial. 2x((-30 + x)(15 + -2x)) = 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 '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30Subproblem 3
Set the factor '(15 + -2x)' equal to zero and attempt to solve: Simplifying 15 + -2x = 0 Solving 15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x = 0 + -15 -2x = 0 + -15 Combine like terms: 0 + -15 = -15 -2x = -15 Divide each side by '-2'. x = 7.5 Simplifying x = 7.5Solution
x = {0, 30, 7.5}
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