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Simplifying x2 + -49 = (x + c)(x + d) Reorder the terms: -49 + x2 = (x + c)(x + d) Reorder the terms: -49 + x2 = (c + x)(x + d) Reorder the terms: -49 + x2 = (c + x)(d + x) Multiply (c + x) * (d + x) -49 + x2 = (c(d + x) + x(d + x)) -49 + x2 = ((d * c + x * c) + x(d + x)) -49 + x2 = ((cd + cx) + x(d + x)) -49 + x2 = (cd + cx + (d * x + x * x)) -49 + x2 = (cd + cx + (dx + x2)) -49 + x2 = (cd + cx + dx + x2) Add '-1x2' to each side of the equation. -49 + x2 + -1x2 = cd + cx + dx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 + 0 = cd + cx + dx + x2 + -1x2 -49 = cd + cx + dx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 = cd + cx + dx + 0 -49 = cd + cx + dx Solving -49 = cd + cx + dx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1cd' to each side of the equation. -49 + -1cd = cd + cx + -1cd + dx Reorder the terms: -49 + -1cd = cd + -1cd + cx + dx Combine like terms: cd + -1cd = 0 -49 + -1cd = 0 + cx + dx -49 + -1cd = cx + dx Add '-1cx' to each side of the equation. -49 + -1cd + -1cx = cx + -1cx + dx Combine like terms: cx + -1cx = 0 -49 + -1cd + -1cx = 0 + dx -49 + -1cd + -1cx = dx Add '49' to each side of the equation. -49 + -1cd + 49 + -1cx = 49 + dx Reorder the terms: -49 + 49 + -1cd + -1cx = 49 + dx Combine like terms: -49 + 49 = 0 0 + -1cd + -1cx = 49 + dx -1cd + -1cx = 49 + dx Reorder the terms: -49 + -1cd + -1cx + -1dx = 49 + dx + -49 + -1dx Reorder the terms: -49 + -1cd + -1cx + -1dx = 49 + -49 + dx + -1dx Combine like terms: 49 + -49 = 0 -49 + -1cd + -1cx + -1dx = 0 + dx + -1dx -49 + -1cd + -1cx + -1dx = dx + -1dx Combine like terms: dx + -1dx = 0 -49 + -1cd + -1cx + -1dx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + cd + cx + dx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(49 + cd + cx + dx)' equal to zero and attempt to solve: Simplifying 49 + cd + cx + dx = 0 Solving 49 + cd + cx + dx = 0 Move all terms containing c to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + cd + cx + -49 + dx = 0 + -49 Reorder the terms: 49 + -49 + cd + cx + dx = 0 + -49 Combine like terms: 49 + -49 = 0 0 + cd + cx + dx = 0 + -49 cd + cx + dx = 0 + -49 Combine like terms: 0 + -49 = -49 cd + cx + dx = -49 Add '-1dx' to each side of the equation. cd + cx + dx + -1dx = -49 + -1dx Combine like terms: dx + -1dx = 0 cd + cx + 0 = -49 + -1dx cd + cx = -49 + -1dx 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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