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Simplifying 5x2 + 30 = 8x2 + x Reorder the terms: 30 + 5x2 = 8x2 + x Reorder the terms: 30 + 5x2 = x + 8x2 Solving 30 + 5x2 = x + 8x2 Solving for variable 'x'. Reorder the terms: 30 + -1x + 5x2 + -8x2 = x + 8x2 + -1x + -8x2 Combine like terms: 5x2 + -8x2 = -3x2 30 + -1x + -3x2 = x + 8x2 + -1x + -8x2 Reorder the terms: 30 + -1x + -3x2 = x + -1x + 8x2 + -8x2 Combine like terms: x + -1x = 0 30 + -1x + -3x2 = 0 + 8x2 + -8x2 30 + -1x + -3x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 30 + -1x + -3x2 = 0 Factor a trinomial. (3 + -1x)(10 + 3x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(10 + 3x)' equal to zero and attempt to solve: Simplifying 10 + 3x = 0 Solving 10 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3x = 0 + -10 3x = 0 + -10 Combine like terms: 0 + -10 = -10 3x = -10 Divide each side by '3'. x = -3.333333333 Simplifying x = -3.333333333Solution
x = {3, -3.333333333}
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