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Simplifying (-5b + -7)(4b + 3) + -1(-10b + 7)(-5b + -7) = 0 Reorder the terms: (-7 + -5b)(4b + 3) + -1(-10b + 7)(-5b + -7) = 0 Reorder the terms: (-7 + -5b)(3 + 4b) + -1(-10b + 7)(-5b + -7) = 0 Multiply (-7 + -5b) * (3 + 4b) (-7(3 + 4b) + -5b * (3 + 4b)) + -1(-10b + 7)(-5b + -7) = 0 ((3 * -7 + 4b * -7) + -5b * (3 + 4b)) + -1(-10b + 7)(-5b + -7) = 0 ((-21 + -28b) + -5b * (3 + 4b)) + -1(-10b + 7)(-5b + -7) = 0 (-21 + -28b + (3 * -5b + 4b * -5b)) + -1(-10b + 7)(-5b + -7) = 0 (-21 + -28b + (-15b + -20b2)) + -1(-10b + 7)(-5b + -7) = 0 Combine like terms: -28b + -15b = -43b (-21 + -43b + -20b2) + -1(-10b + 7)(-5b + -7) = 0 Reorder the terms: -21 + -43b + -20b2 + -1(7 + -10b)(-5b + -7) = 0 Reorder the terms: -21 + -43b + -20b2 + -1(7 + -10b)(-7 + -5b) = 0 Multiply (7 + -10b) * (-7 + -5b) -21 + -43b + -20b2 + -1(7(-7 + -5b) + -10b * (-7 + -5b)) = 0 -21 + -43b + -20b2 + -1((-7 * 7 + -5b * 7) + -10b * (-7 + -5b)) = 0 -21 + -43b + -20b2 + -1((-49 + -35b) + -10b * (-7 + -5b)) = 0 -21 + -43b + -20b2 + -1(-49 + -35b + (-7 * -10b + -5b * -10b)) = 0 -21 + -43b + -20b2 + -1(-49 + -35b + (70b + 50b2)) = 0 Combine like terms: -35b + 70b = 35b -21 + -43b + -20b2 + -1(-49 + 35b + 50b2) = 0 -21 + -43b + -20b2 + (-49 * -1 + 35b * -1 + 50b2 * -1) = 0 -21 + -43b + -20b2 + (49 + -35b + -50b2) = 0 Reorder the terms: -21 + 49 + -43b + -35b + -20b2 + -50b2 = 0 Combine like terms: -21 + 49 = 28 28 + -43b + -35b + -20b2 + -50b2 = 0 Combine like terms: -43b + -35b = -78b 28 + -78b + -20b2 + -50b2 = 0 Combine like terms: -20b2 + -50b2 = -70b2 28 + -78b + -70b2 = 0 Solving 28 + -78b + -70b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -39b + -35b2) = 0 Factor a trinomial. 2((2 + -7b)(7 + 5b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -7b)' equal to zero and attempt to solve: Simplifying 2 + -7b = 0 Solving 2 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7b = 0 + -2 -7b = 0 + -2 Combine like terms: 0 + -2 = -2 -7b = -2 Divide each side by '-7'. b = 0.2857142857 Simplifying b = 0.2857142857Subproblem 2
Set the factor '(7 + 5b)' equal to zero and attempt to solve: Simplifying 7 + 5b = 0 Solving 7 + 5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5b = 0 + -7 5b = 0 + -7 Combine like terms: 0 + -7 = -7 5b = -7 Divide each side by '5'. b = -1.4 Simplifying b = -1.4Solution
b = {0.2857142857, -1.4}
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