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Simplifying 0 = 9x2 + -61x + 100 Reorder the terms: 0 = 100 + -61x + 9x2 Solving 0 = 100 + -61x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + 61x + -9x2 = 100 + -61x + 9x2 + -100 + 61x + -9x2 Reorder the terms: -100 + 61x + -9x2 = 100 + -100 + -61x + 61x + 9x2 + -9x2 Combine like terms: 100 + -100 = 0 -100 + 61x + -9x2 = 0 + -61x + 61x + 9x2 + -9x2 -100 + 61x + -9x2 = -61x + 61x + 9x2 + -9x2 Combine like terms: -61x + 61x = 0 -100 + 61x + -9x2 = 0 + 9x2 + -9x2 -100 + 61x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -100 + 61x + -9x2 = 0 Factor a trinomial. (-4 + x)(25 + -9x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
Set the factor '(25 + -9x)' equal to zero and attempt to solve: Simplifying 25 + -9x = 0 Solving 25 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -9x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -9x = 0 + -25 -9x = 0 + -25 Combine like terms: 0 + -25 = -25 -9x = -25 Divide each side by '-9'. x = 2.777777778 Simplifying x = 2.777777778Solution
x = {4, 2.777777778}
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