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Simplifying x2 + bx + -35 = (x + 5)(x + -7) Reorder the terms: -35 + bx + x2 = (x + 5)(x + -7) Reorder the terms: -35 + bx + x2 = (5 + x)(x + -7) Reorder the terms: -35 + bx + x2 = (5 + x)(-7 + x) Multiply (5 + x) * (-7 + x) -35 + bx + x2 = (5(-7 + x) + x(-7 + x)) -35 + bx + x2 = ((-7 * 5 + x * 5) + x(-7 + x)) -35 + bx + x2 = ((-35 + 5x) + x(-7 + x)) -35 + bx + x2 = (-35 + 5x + (-7 * x + x * x)) -35 + bx + x2 = (-35 + 5x + (-7x + x2)) Combine like terms: 5x + -7x = -2x -35 + bx + x2 = (-35 + -2x + x2) Add '35' to each side of the equation. -35 + bx + 35 + x2 = -35 + -2x + 35 + x2 Reorder the terms: -35 + 35 + bx + x2 = -35 + -2x + 35 + x2 Combine like terms: -35 + 35 = 0 0 + bx + x2 = -35 + -2x + 35 + x2 bx + x2 = -35 + -2x + 35 + x2 Reorder the terms: bx + x2 = -35 + 35 + -2x + x2 Combine like terms: -35 + 35 = 0 bx + x2 = 0 + -2x + x2 bx + x2 = -2x + x2 Add '-1x2' to each side of the equation. bx + x2 + -1x2 = -2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 bx + 0 = -2x + x2 + -1x2 bx = -2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 bx = -2x + 0 bx = -2x Solving bx = -2x Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Divide each side by 'x'. b = -2 Simplifying b = -2
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