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Simplifying 7(-10x + 29) = 1(5x + -7)(10x + 1) Reorder the terms: 7(29 + -10x) = 1(5x + -7)(10x + 1) (29 * 7 + -10x * 7) = 1(5x + -7)(10x + 1) (203 + -70x) = 1(5x + -7)(10x + 1) Reorder the terms: 203 + -70x = 1(-7 + 5x)(10x + 1) Reorder the terms: 203 + -70x = 1(-7 + 5x)(1 + 10x) Multiply (-7 + 5x) * (1 + 10x) 203 + -70x = 1(-7(1 + 10x) + 5x * (1 + 10x)) 203 + -70x = 1((1 * -7 + 10x * -7) + 5x * (1 + 10x)) 203 + -70x = 1((-7 + -70x) + 5x * (1 + 10x)) 203 + -70x = 1(-7 + -70x + (1 * 5x + 10x * 5x)) 203 + -70x = 1(-7 + -70x + (5x + 50x2)) Combine like terms: -70x + 5x = -65x 203 + -70x = 1(-7 + -65x + 50x2) 203 + -70x = (-7 * 1 + -65x * 1 + 50x2 * 1) 203 + -70x = (-7 + -65x + 50x2) Solving 203 + -70x = -7 + -65x + 50x2 Solving for variable 'x'. Reorder the terms: 203 + 7 + -70x + 65x + -50x2 = -7 + -65x + 50x2 + 7 + 65x + -50x2 Combine like terms: 203 + 7 = 210 210 + -70x + 65x + -50x2 = -7 + -65x + 50x2 + 7 + 65x + -50x2 Combine like terms: -70x + 65x = -5x 210 + -5x + -50x2 = -7 + -65x + 50x2 + 7 + 65x + -50x2 Reorder the terms: 210 + -5x + -50x2 = -7 + 7 + -65x + 65x + 50x2 + -50x2 Combine like terms: -7 + 7 = 0 210 + -5x + -50x2 = 0 + -65x + 65x + 50x2 + -50x2 210 + -5x + -50x2 = -65x + 65x + 50x2 + -50x2 Combine like terms: -65x + 65x = 0 210 + -5x + -50x2 = 0 + 50x2 + -50x2 210 + -5x + -50x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 210 + -5x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(42 + -1x + -10x2) = 0 Factor a trinomial. 5((2 + -1x)(21 + 10x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(21 + 10x)' equal to zero and attempt to solve: Simplifying 21 + 10x = 0 Solving 21 + 10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 10x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 10x = 0 + -21 10x = 0 + -21 Combine like terms: 0 + -21 = -21 10x = -21 Divide each side by '10'. x = -2.1 Simplifying x = -2.1Solution
x = {2, -2.1}
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