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Simplifying 0 = 2x2 + -28x + 98 Reorder the terms: 0 = 98 + -28x + 2x2 Solving 0 = 98 + -28x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -98 = -98 -98 + 28x + -2x2 = 98 + -28x + 2x2 + -98 + 28x + -2x2 Reorder the terms: -98 + 28x + -2x2 = 98 + -98 + -28x + 28x + 2x2 + -2x2 Combine like terms: 98 + -98 = 0 -98 + 28x + -2x2 = 0 + -28x + 28x + 2x2 + -2x2 -98 + 28x + -2x2 = -28x + 28x + 2x2 + -2x2 Combine like terms: -28x + 28x = 0 -98 + 28x + -2x2 = 0 + 2x2 + -2x2 -98 + 28x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -98 + 28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 14x + -1x2) = 0 Factor a trinomial. 2((-7 + x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {7, 7}
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