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Simplifying x2 + -2x + -3 = (x + g)(x + h) Reorder the terms: -3 + -2x + x2 = (x + g)(x + h) Reorder the terms: -3 + -2x + x2 = (g + x)(x + h) Reorder the terms: -3 + -2x + x2 = (g + x)(h + x) Multiply (g + x) * (h + x) -3 + -2x + x2 = (g(h + x) + x(h + x)) -3 + -2x + x2 = ((h * g + x * g) + x(h + x)) -3 + -2x + x2 = ((gh + gx) + x(h + x)) -3 + -2x + x2 = (gh + gx + (h * x + x * x)) -3 + -2x + x2 = (gh + gx + (hx + x2)) -3 + -2x + x2 = (gh + gx + hx + x2) Add '-1x2' to each side of the equation. -3 + -2x + x2 + -1x2 = gh + gx + hx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + -2x + 0 = gh + gx + hx + x2 + -1x2 -3 + -2x = gh + gx + hx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + -2x = gh + gx + hx + 0 -3 + -2x = gh + gx + hx Solving -3 + -2x = gh + gx + hx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1gx' to each side of the equation. -3 + -1gx + -2x = gh + gx + -1gx + hx Combine like terms: gx + -1gx = 0 -3 + -1gx + -2x = gh + 0 + hx -3 + -1gx + -2x = gh + hx Add '-1hx' to each side of the equation. -3 + -1gx + -1hx + -2x = gh + hx + -1hx Combine like terms: hx + -1hx = 0 -3 + -1gx + -1hx + -2x = gh + 0 -3 + -1gx + -1hx + -2x = gh Add '3' to each side of the equation. -3 + -1gx + -1hx + 3 + -2x = 3 + gh Reorder the terms: -3 + 3 + -1gx + -1hx + -2x = 3 + gh Combine like terms: -3 + 3 = 0 0 + -1gx + -1hx + -2x = 3 + gh -1gx + -1hx + -2x = 3 + gh Reorder the terms: -3 + -1gh + -1gx + -1hx + -2x = 3 + gh + -3 + -1gh Reorder the terms: -3 + -1gh + -1gx + -1hx + -2x = 3 + -3 + gh + -1gh Combine like terms: 3 + -3 = 0 -3 + -1gh + -1gx + -1hx + -2x = 0 + gh + -1gh -3 + -1gh + -1gx + -1hx + -2x = gh + -1gh Combine like terms: gh + -1gh = 0 -3 + -1gh + -1gx + -1hx + -2x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + gh + gx + hx + 2x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + gh + gx + hx + 2x)' equal to zero and attempt to solve: Simplifying 3 + gh + gx + hx + 2x = 0 Solving 3 + gh + gx + hx + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + gh + gx + hx + -3 + 2x = 0 + -3 Reorder the terms: 3 + -3 + gh + gx + hx + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + gh + gx + hx + 2x = 0 + -3 gh + gx + hx + 2x = 0 + -3 Combine like terms: 0 + -3 = -3 gh + gx + hx + 2x = -3 Add '-1gh' to each side of the equation. gh + gx + hx + -1gh + 2x = -3 + -1gh Reorder the terms: gh + -1gh + gx + hx + 2x = -3 + -1gh Combine like terms: gh + -1gh = 0 0 + gx + hx + 2x = -3 + -1gh gx + hx + 2x = -3 + -1gh The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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