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Simplifying (2b + -14)(14b + -2) = 0 Reorder the terms: (-14 + 2b)(14b + -2) = 0 Reorder the terms: (-14 + 2b)(-2 + 14b) = 0 Multiply (-14 + 2b) * (-2 + 14b) (-14(-2 + 14b) + 2b * (-2 + 14b)) = 0 ((-2 * -14 + 14b * -14) + 2b * (-2 + 14b)) = 0 ((28 + -196b) + 2b * (-2 + 14b)) = 0 (28 + -196b + (-2 * 2b + 14b * 2b)) = 0 (28 + -196b + (-4b + 28b2)) = 0 Combine like terms: -196b + -4b = -200b (28 + -200b + 28b2) = 0 Solving 28 + -200b + 28b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -50b + 7b2) = 0 Factor a trinomial. 4((1 + -7b)(7 + -1b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -7b)' equal to zero and attempt to solve: Simplifying 1 + -7b = 0 Solving 1 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7b = 0 + -1 -7b = 0 + -1 Combine like terms: 0 + -1 = -1 -7b = -1 Divide each side by '-7'. b = 0.1428571429 Simplifying b = 0.1428571429Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve: Simplifying 7 + -1b = 0 Solving 7 + -1b = 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 + -1b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1b = 0 + -7 -1b = 0 + -7 Combine like terms: 0 + -7 = -7 -1b = -7 Divide each side by '-1'. b = 7 Simplifying b = 7Solution
b = {0.1428571429, 7}
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