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Simplifying x2 + 10x + 24 = (a + x)(b + x) Reorder the terms: 24 + 10x + x2 = (a + x)(b + x) Multiply (a + x) * (b + x) 24 + 10x + x2 = (a(b + x) + x(b + x)) 24 + 10x + x2 = ((b * a + x * a) + x(b + x)) 24 + 10x + x2 = ((ab + ax) + x(b + x)) 24 + 10x + x2 = (ab + ax + (b * x + x * x)) 24 + 10x + x2 = (ab + ax + (bx + x2)) 24 + 10x + x2 = (ab + ax + bx + x2) Add '-1x2' to each side of the equation. 24 + 10x + x2 + -1x2 = ab + ax + bx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + 10x + 0 = ab + ax + bx + x2 + -1x2 24 + 10x = ab + ax + bx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + 10x = ab + ax + bx + 0 24 + 10x = ab + ax + bx Solving 24 + 10x = ab + ax + bx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1ax' to each side of the equation. 24 + -1ax + 10x = ab + ax + -1ax + bx Combine like terms: ax + -1ax = 0 24 + -1ax + 10x = ab + 0 + bx 24 + -1ax + 10x = ab + bx Add '-1bx' to each side of the equation. 24 + -1ax + -1bx + 10x = ab + bx + -1bx Combine like terms: bx + -1bx = 0 24 + -1ax + -1bx + 10x = ab + 0 24 + -1ax + -1bx + 10x = ab Add '-24' to each side of the equation. 24 + -1ax + -1bx + -24 + 10x = -24 + ab Reorder the terms: 24 + -24 + -1ax + -1bx + 10x = -24 + ab Combine like terms: 24 + -24 = 0 0 + -1ax + -1bx + 10x = -24 + ab -1ax + -1bx + 10x = -24 + ab Reorder the terms: 24 + -1ab + -1ax + -1bx + 10x = -24 + ab + 24 + -1ab Reorder the terms: 24 + -1ab + -1ax + -1bx + 10x = -24 + 24 + ab + -1ab Combine like terms: -24 + 24 = 0 24 + -1ab + -1ax + -1bx + 10x = 0 + ab + -1ab 24 + -1ab + -1ax + -1bx + 10x = ab + -1ab Combine like terms: ab + -1ab = 0 24 + -1ab + -1ax + -1bx + 10x = 0 The solution to this equation could not be determined.
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