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Simplifying (350 + -10a)(a + -21) = 400 Reorder the terms: (350 + -10a)(-21 + a) = 400 Multiply (350 + -10a) * (-21 + a) (350(-21 + a) + -10a * (-21 + a)) = 400 ((-21 * 350 + a * 350) + -10a * (-21 + a)) = 400 ((-7350 + 350a) + -10a * (-21 + a)) = 400 (-7350 + 350a + (-21 * -10a + a * -10a)) = 400 (-7350 + 350a + (210a + -10a2)) = 400 Combine like terms: 350a + 210a = 560a (-7350 + 560a + -10a2) = 400 Solving -7350 + 560a + -10a2 = 400 Solving for variable 'a'. Reorder the terms: -7350 + -400 + 560a + -10a2 = 400 + -400 Combine like terms: -7350 + -400 = -7750 -7750 + 560a + -10a2 = 400 + -400 Combine like terms: 400 + -400 = 0 -7750 + 560a + -10a2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-775 + 56a + -1a2) = 0 Factor a trinomial. 10((-31 + a)(25 + -1a)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-31 + a)' equal to zero and attempt to solve: Simplifying -31 + a = 0 Solving -31 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + a = 0 + 31 Combine like terms: -31 + 31 = 0 0 + a = 0 + 31 a = 0 + 31 Combine like terms: 0 + 31 = 31 a = 31 Simplifying a = 31Subproblem 2
Set the factor '(25 + -1a)' equal to zero and attempt to solve: Simplifying 25 + -1a = 0 Solving 25 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1a = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1a = 0 + -25 -1a = 0 + -25 Combine like terms: 0 + -25 = -25 -1a = -25 Divide each side by '-1'. a = 25 Simplifying a = 25Solution
a = {31, 25}
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