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Simplifying 5x2 + 17x + 14 = (x + a)(5x + b) Reorder the terms: 14 + 17x + 5x2 = (x + a)(5x + b) Reorder the terms: 14 + 17x + 5x2 = (a + x)(5x + b) Reorder the terms: 14 + 17x + 5x2 = (a + x)(b + 5x) Multiply (a + x) * (b + 5x) 14 + 17x + 5x2 = (a(b + 5x) + x(b + 5x)) 14 + 17x + 5x2 = ((b * a + 5x * a) + x(b + 5x)) 14 + 17x + 5x2 = ((ab + 5ax) + x(b + 5x)) 14 + 17x + 5x2 = (ab + 5ax + (b * x + 5x * x)) 14 + 17x + 5x2 = (ab + 5ax + (bx + 5x2)) 14 + 17x + 5x2 = (ab + 5ax + bx + 5x2) Add '-5x2' to each side of the equation. 14 + 17x + 5x2 + -5x2 = ab + 5ax + bx + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 14 + 17x + 0 = ab + 5ax + bx + 5x2 + -5x2 14 + 17x = ab + 5ax + bx + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 14 + 17x = ab + 5ax + bx + 0 14 + 17x = ab + 5ax + bx Solving 14 + 17x = ab + 5ax + bx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5ax' to each side of the equation. 14 + -5ax + 17x = ab + 5ax + -5ax + bx Combine like terms: 5ax + -5ax = 0 14 + -5ax + 17x = ab + 0 + bx 14 + -5ax + 17x = ab + bx Add '-1bx' to each side of the equation. 14 + -5ax + -1bx + 17x = ab + bx + -1bx Combine like terms: bx + -1bx = 0 14 + -5ax + -1bx + 17x = ab + 0 14 + -5ax + -1bx + 17x = ab Add '-14' to each side of the equation. 14 + -5ax + -1bx + -14 + 17x = -14 + ab Reorder the terms: 14 + -14 + -5ax + -1bx + 17x = -14 + ab Combine like terms: 14 + -14 = 0 0 + -5ax + -1bx + 17x = -14 + ab -5ax + -1bx + 17x = -14 + ab Reorder the terms: 14 + -1ab + -5ax + -1bx + 17x = -14 + ab + 14 + -1ab Reorder the terms: 14 + -1ab + -5ax + -1bx + 17x = -14 + 14 + ab + -1ab Combine like terms: -14 + 14 = 0 14 + -1ab + -5ax + -1bx + 17x = 0 + ab + -1ab 14 + -1ab + -5ax + -1bx + 17x = ab + -1ab Combine like terms: ab + -1ab = 0 14 + -1ab + -5ax + -1bx + 17x = 0 The solution to this equation could not be determined.
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