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Simplifying 55x2 + 228x + -90 = 7x2 + 6x Reorder the terms: -90 + 228x + 55x2 = 7x2 + 6x Reorder the terms: -90 + 228x + 55x2 = 6x + 7x2 Solving -90 + 228x + 55x2 = 6x + 7x2 Solving for variable 'x'. Reorder the terms: -90 + 228x + -6x + 55x2 + -7x2 = 6x + 7x2 + -6x + -7x2 Combine like terms: 228x + -6x = 222x -90 + 222x + 55x2 + -7x2 = 6x + 7x2 + -6x + -7x2 Combine like terms: 55x2 + -7x2 = 48x2 -90 + 222x + 48x2 = 6x + 7x2 + -6x + -7x2 Reorder the terms: -90 + 222x + 48x2 = 6x + -6x + 7x2 + -7x2 Combine like terms: 6x + -6x = 0 -90 + 222x + 48x2 = 0 + 7x2 + -7x2 -90 + 222x + 48x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -90 + 222x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 37x + 8x2) = 0 Factor a trinomial. 6((-5 + -1x)(3 + -8x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Solution
x = {-5, 0.375}
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