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Simplifying 0 = -14x2 + 1120x + -9800 Reorder the terms: 0 = -9800 + 1120x + -14x2 Solving 0 = -9800 + 1120x + -14x2 Solving for variable 'x'. Combine like terms: 0 + 9800 = 9800 9800 + -1120x + 14x2 = -9800 + 1120x + -14x2 + 9800 + -1120x + 14x2 Reorder the terms: 9800 + -1120x + 14x2 = -9800 + 9800 + 1120x + -1120x + -14x2 + 14x2 Combine like terms: -9800 + 9800 = 0 9800 + -1120x + 14x2 = 0 + 1120x + -1120x + -14x2 + 14x2 9800 + -1120x + 14x2 = 1120x + -1120x + -14x2 + 14x2 Combine like terms: 1120x + -1120x = 0 9800 + -1120x + 14x2 = 0 + -14x2 + 14x2 9800 + -1120x + 14x2 = -14x2 + 14x2 Combine like terms: -14x2 + 14x2 = 0 9800 + -1120x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '14'. 14(700 + -80x + x2) = 0 Factor a trinomial. 14((10 + -1x)(70 + -1x)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 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 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70Solution
x = {10, 70}
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