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Simplifying 7x + 9 = 49x2 + 126x + 81 Reorder the terms: 9 + 7x = 49x2 + 126x + 81 Reorder the terms: 9 + 7x = 81 + 126x + 49x2 Solving 9 + 7x = 81 + 126x + 49x2 Solving for variable 'x'. Reorder the terms: 9 + -81 + 7x + -126x + -49x2 = 81 + 126x + 49x2 + -81 + -126x + -49x2 Combine like terms: 9 + -81 = -72 -72 + 7x + -126x + -49x2 = 81 + 126x + 49x2 + -81 + -126x + -49x2 Combine like terms: 7x + -126x = -119x -72 + -119x + -49x2 = 81 + 126x + 49x2 + -81 + -126x + -49x2 Reorder the terms: -72 + -119x + -49x2 = 81 + -81 + 126x + -126x + 49x2 + -49x2 Combine like terms: 81 + -81 = 0 -72 + -119x + -49x2 = 0 + 126x + -126x + 49x2 + -49x2 -72 + -119x + -49x2 = 126x + -126x + 49x2 + -49x2 Combine like terms: 126x + -126x = 0 -72 + -119x + -49x2 = 0 + 49x2 + -49x2 -72 + -119x + -49x2 = 49x2 + -49x2 Combine like terms: 49x2 + -49x2 = 0 -72 + -119x + -49x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(72 + 119x + 49x2) = 0 Factor a trinomial. -1((9 + 7x)(8 + 7x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 7x)' equal to zero and attempt to solve: Simplifying 9 + 7x = 0 Solving 9 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7x = 0 + -9 7x = 0 + -9 Combine like terms: 0 + -9 = -9 7x = -9 Divide each side by '7'. x = -1.285714286 Simplifying x = -1.285714286Subproblem 2
Set the factor '(8 + 7x)' equal to zero and attempt to solve: Simplifying 8 + 7x = 0 Solving 8 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7x = 0 + -8 7x = 0 + -8 Combine like terms: 0 + -8 = -8 7x = -8 Divide each side by '7'. x = -1.142857143 Simplifying x = -1.142857143Solution
x = {-1.285714286, -1.142857143}
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