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Simplifying 12x2 + -70x + 101 = 3 Reorder the terms: 101 + -70x + 12x2 = 3 Solving 101 + -70x + 12x2 = 3 Solving for variable 'x'. Reorder the terms: 101 + -3 + -70x + 12x2 = 3 + -3 Combine like terms: 101 + -3 = 98 98 + -70x + 12x2 = 3 + -3 Combine like terms: 3 + -3 = 0 98 + -70x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -35x + 6x2) = 0 Factor a trinomial. 2((7 + -3x)(7 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {2.333333333, 3.5}
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