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Simplifying x3 + 15x2 = x2 + -49x Reorder the terms: 15x2 + x3 = x2 + -49x Reorder the terms: 15x2 + x3 = -49x + x2 Solving 15x2 + x3 = -49x + x2 Solving for variable 'x'. Reorder the terms: 49x + 15x2 + -1x2 + x3 = -49x + x2 + 49x + -1x2 Combine like terms: 15x2 + -1x2 = 14x2 49x + 14x2 + x3 = -49x + x2 + 49x + -1x2 Reorder the terms: 49x + 14x2 + x3 = -49x + 49x + x2 + -1x2 Combine like terms: -49x + 49x = 0 49x + 14x2 + x3 = 0 + x2 + -1x2 49x + 14x2 + x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 49x + 14x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(49 + 14x + x2) = 0 Factor a trinomial. x((7 + x)(7 + x)) = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 3
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {0, -7, -7}
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