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Simplifying 14x3 = x2 + 4x Reorder the terms: 14x3 = 4x + x2 Solving 14x3 = 4x + x2 Solving for variable 'x'. Reorder the terms: -4x + -1x2 + 14x3 = 4x + x2 + -4x + -1x2 Reorder the terms: -4x + -1x2 + 14x3 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -4x + -1x2 + 14x3 = 0 + x2 + -1x2 -4x + -1x2 + 14x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4x + -1x2 + 14x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -1x + 14x2) = 0 Factor a trinomial. x((-1 + -2x)(4 + -7x)) = 0Subproblem 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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Solution
x = {0, -0.5, 0.5714285714}
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