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Simplifying x3 + -64 = (x + a)(x2 + bx + c) Reorder the terms: -64 + x3 = (x + a)(x2 + bx + c) Reorder the terms: -64 + x3 = (a + x)(x2 + bx + c) Reorder the terms: -64 + x3 = (a + x)(bx + c + x2) Multiply (a + x) * (bx + c + x2) -64 + x3 = (a(bx + c + x2) + x(bx + c + x2)) -64 + x3 = ((bx * a + c * a + x2 * a) + x(bx + c + x2)) -64 + x3 = ((abx + ac + ax2) + x(bx + c + x2)) -64 + x3 = (abx + ac + ax2 + (bx * x + c * x + x2 * x)) -64 + x3 = (abx + ac + ax2 + (bx2 + cx + x3)) -64 + x3 = (abx + ac + ax2 + bx2 + cx + x3) Add '-1x3' to each side of the equation. -64 + x3 + -1x3 = abx + ac + ax2 + bx2 + cx + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -64 + 0 = abx + ac + ax2 + bx2 + cx + x3 + -1x3 -64 = abx + ac + ax2 + bx2 + cx + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -64 = abx + ac + ax2 + bx2 + cx + 0 -64 = abx + ac + ax2 + bx2 + cx Solving -64 = abx + ac + ax2 + bx2 + cx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1abx' to each side of the equation. -64 + -1abx = abx + ac + ax2 + bx2 + -1abx + cx Reorder the terms: -64 + -1abx = abx + -1abx + ac + ax2 + bx2 + cx Combine like terms: abx + -1abx = 0 -64 + -1abx = 0 + ac + ax2 + bx2 + cx -64 + -1abx = ac + ax2 + bx2 + cx Add '-1ac' to each side of the equation. -64 + -1abx + -1ac = ac + ax2 + bx2 + -1ac + cx Reorder the terms: -64 + -1abx + -1ac = ac + -1ac + ax2 + bx2 + cx Combine like terms: ac + -1ac = 0 -64 + -1abx + -1ac = 0 + ax2 + bx2 + cx -64 + -1abx + -1ac = ax2 + bx2 + cx Add '-1ax2' to each side of the equation. -64 + -1abx + -1ac + -1ax2 = ax2 + bx2 + -1ax2 + cx Reorder the terms: -64 + -1abx + -1ac + -1ax2 = ax2 + -1ax2 + bx2 + cx Combine like terms: ax2 + -1ax2 = 0 -64 + -1abx + -1ac + -1ax2 = 0 + bx2 + cx -64 + -1abx + -1ac + -1ax2 = bx2 + cx Add '64' to each side of the equation. -64 + -1abx + -1ac + 64 + -1ax2 = bx2 + 64 + cx Reorder the terms: -64 + 64 + -1abx + -1ac + -1ax2 = bx2 + 64 + cx Combine like terms: -64 + 64 = 0 0 + -1abx + -1ac + -1ax2 = bx2 + 64 + cx -1abx + -1ac + -1ax2 = bx2 + 64 + cx Reorder the terms: -1abx + -1ac + -1ax2 = 64 + bx2 + cx Reorder the terms: -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 64 + bx2 + cx + -64 + -1bx2 + -1cx Reorder the terms: -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 64 + -64 + bx2 + -1bx2 + cx + -1cx Combine like terms: 64 + -64 = 0 -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0 + bx2 + -1bx2 + cx + -1cx -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = bx2 + -1bx2 + cx + -1cx Combine like terms: bx2 + -1bx2 = 0 -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0 + cx + -1cx -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = cx + -1cx Combine like terms: cx + -1cx = 0 -64 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(64 + abx + ac + ax2 + bx2 + cx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(64 + abx + ac + ax2 + bx2 + cx)' equal to zero and attempt to solve: Simplifying 64 + abx + ac + ax2 + bx2 + cx = 0 Solving 64 + abx + ac + ax2 + bx2 + cx = 0 Move all terms containing a to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + abx + ac + ax2 + bx2 + -64 + cx = 0 + -64 Reorder the terms: 64 + -64 + abx + ac + ax2 + bx2 + cx = 0 + -64 Combine like terms: 64 + -64 = 0 0 + abx + ac + ax2 + bx2 + cx = 0 + -64 abx + ac + ax2 + bx2 + cx = 0 + -64 Combine like terms: 0 + -64 = -64 abx + ac + ax2 + bx2 + cx = -64 Add '-1bx2' to each side of the equation. abx + ac + ax2 + bx2 + -1bx2 + cx = -64 + -1bx2 Combine like terms: bx2 + -1bx2 = 0 abx + ac + ax2 + 0 + cx = -64 + -1bx2 abx + ac + ax2 + cx = -64 + -1bx2 Add '-1cx' to each side of the equation. abx + ac + ax2 + cx + -1cx = -64 + -1bx2 + -1cx Combine like terms: cx + -1cx = 0 abx + ac + ax2 + 0 = -64 + -1bx2 + -1cx abx + ac + ax2 = -64 + -1bx2 + -1cx 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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