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Simplifying 15x4 = 11x3 + 14x2 Reorder the terms: 15x4 = 14x2 + 11x3 Solving 15x4 = 14x2 + 11x3 Solving for variable 'x'. Reorder the terms: -14x2 + -11x3 + 15x4 = 14x2 + 11x3 + -14x2 + -11x3 Reorder the terms: -14x2 + -11x3 + 15x4 = 14x2 + -14x2 + 11x3 + -11x3 Combine like terms: 14x2 + -14x2 = 0 -14x2 + -11x3 + 15x4 = 0 + 11x3 + -11x3 -14x2 + -11x3 + 15x4 = 11x3 + -11x3 Combine like terms: 11x3 + -11x3 = 0 -14x2 + -11x3 + 15x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-14 + -11x + 15x2) = 0 Factor a trinomial. x2((-2 + -3x)(7 + -5x)) = 0Subproblem 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 '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 3
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {0, -0.6666666667, 1.4}
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