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Simplifying x2 + -1bx + -21 = (x + p)(x + -7) Reorder the terms: -21 + -1bx + x2 = (x + p)(x + -7) Reorder the terms: -21 + -1bx + x2 = (p + x)(x + -7) Reorder the terms: -21 + -1bx + x2 = (p + x)(-7 + x) Multiply (p + x) * (-7 + x) -21 + -1bx + x2 = (p(-7 + x) + x(-7 + x)) -21 + -1bx + x2 = ((-7 * p + x * p) + x(-7 + x)) -21 + -1bx + x2 = ((-7p + px) + x(-7 + x)) -21 + -1bx + x2 = (-7p + px + (-7 * x + x * x)) -21 + -1bx + x2 = (-7p + px + (-7x + x2)) -21 + -1bx + x2 = (-7p + px + -7x + x2) Add '-1x2' to each side of the equation. -21 + -1bx + x2 + -1x2 = -7p + px + -7x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + -1bx + 0 = -7p + px + -7x + x2 + -1x2 -21 + -1bx = -7p + px + -7x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + -1bx = -7p + px + -7x + 0 -21 + -1bx = -7p + px + -7x Solving -21 + -1bx = -7p + px + -7x Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1bx = -7p + px + 21 + -7x Combine like terms: -21 + 21 = 0 0 + -1bx = -7p + px + 21 + -7x -1bx = -7p + px + 21 + -7x Reorder the terms: -1bx = 21 + -7p + px + -7x Divide each side by '-1x'. b = -21x-1 + 7px-1 + -1p + 7 Simplifying b = -21x-1 + 7px-1 + -1p + 7 Reorder the terms: b = 7 + -1p + 7px-1 + -21x-1
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