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Simplifying (x + a)(x + b) + -1ab = (x + c)(x + -1c) + c(a + c) Reorder the terms: (a + x)(x + b) + -1ab = (x + c)(x + -1c) + c(a + c) Reorder the terms: (a + x)(b + x) + -1ab = (x + c)(x + -1c) + c(a + c) Multiply (a + x) * (b + x) (a(b + x) + x(b + x)) + -1ab = (x + c)(x + -1c) + c(a + c) ((b * a + x * a) + x(b + x)) + -1ab = (x + c)(x + -1c) + c(a + c) ((ab + ax) + x(b + x)) + -1ab = (x + c)(x + -1c) + c(a + c) (ab + ax + (b * x + x * x)) + -1ab = (x + c)(x + -1c) + c(a + c) (ab + ax + (bx + x2)) + -1ab = (x + c)(x + -1c) + c(a + c) (ab + ax + bx + x2) + -1ab = (x + c)(x + -1c) + c(a + c) Reorder the terms: ab + -1ab + ax + bx + x2 = (x + c)(x + -1c) + c(a + c) Combine like terms: ab + -1ab = 0 0 + ax + bx + x2 = (x + c)(x + -1c) + c(a + c) ax + bx + x2 = (x + c)(x + -1c) + c(a + c) Reorder the terms: ax + bx + x2 = (c + x)(x + -1c) + c(a + c) Reorder the terms: ax + bx + x2 = (c + x)(-1c + x) + c(a + c) Multiply (c + x) * (-1c + x) ax + bx + x2 = (c(-1c + x) + x(-1c + x)) + c(a + c) ax + bx + x2 = ((-1c * c + x * c) + x(-1c + x)) + c(a + c) Reorder the terms: ax + bx + x2 = ((cx + -1c2) + x(-1c + x)) + c(a + c) ax + bx + x2 = ((cx + -1c2) + x(-1c + x)) + c(a + c) ax + bx + x2 = (cx + -1c2 + (-1c * x + x * x)) + c(a + c) ax + bx + x2 = (cx + -1c2 + (-1cx + x2)) + c(a + c) Reorder the terms: ax + bx + x2 = (cx + -1cx + -1c2 + x2) + c(a + c) Combine like terms: cx + -1cx = 0 ax + bx + x2 = (0 + -1c2 + x2) + c(a + c) ax + bx + x2 = (-1c2 + x2) + c(a + c) ax + bx + x2 = -1c2 + x2 + (a * c + c * c) ax + bx + x2 = -1c2 + x2 + (ac + c2) Reorder the terms: ax + bx + x2 = ac + -1c2 + c2 + x2 Combine like terms: -1c2 + c2 = 0 ax + bx + x2 = ac + 0 + x2 ax + bx + x2 = ac + x2 Add '-1x2' to each side of the equation. ax + bx + x2 + -1x2 = ac + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 ax + bx + 0 = ac + x2 + -1x2 ax + bx = ac + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 ax + bx = ac + 0 ax + bx = ac Solving ax + bx = ac Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1ac' to each side of the equation. ax + -1ac + bx = ac + -1ac Reorder the terms: -1ac + ax + bx = ac + -1ac Combine like terms: ac + -1ac = 0 -1ac + ax + bx = 0 Add '-1bx' to each side of the equation. -1ac + ax + bx + -1bx = 0 + -1bx Combine like terms: bx + -1bx = 0 -1ac + ax + 0 = 0 + -1bx -1ac + ax = 0 + -1bx Remove the zero: -1ac + ax = -1bx Combine like terms: -1bx + bx = 0 -1ac + ax + bx = 0 The solution to this equation could not be determined.
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