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Simplifying (-2s + -4)(4s2 + -8S + 16) = 0 Reorder the terms: (-4 + -2s)(4s2 + -8S + 16) = 0 Reorder the terms: (-4 + -2s)(16 + -8S + 4s2) = 0 Multiply (-4 + -2s) * (16 + -8S + 4s2) (-4(16 + -8S + 4s2) + -2s * (16 + -8S + 4s2)) = 0 ((16 * -4 + -8S * -4 + 4s2 * -4) + -2s * (16 + -8S + 4s2)) = 0 ((-64 + 32S + -16s2) + -2s * (16 + -8S + 4s2)) = 0 (-64 + 32S + -16s2 + (16 * -2s + -8S * -2s + 4s2 * -2s)) = 0 (-64 + 32S + -16s2 + (-32s + 16sS + -8s3)) = 0 Reorder the terms: (-64 + 32S + -32s + 16sS + -16s2 + -8s3) = 0 (-64 + 32S + -32s + 16sS + -16s2 + -8s3) = 0 Solving -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 Solving for variable 'S'. Move all terms containing S to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 32S + -32s + 16sS + -16s2 + 64 + -8s3 = 0 + 64 Reorder the terms: -64 + 64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 64 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 64 Combine like terms: 0 + 64 = 64 32S + -32s + 16sS + -16s2 + -8s3 = 64 Add '32s' to each side of the equation. 32S + -32s + 16sS + -16s2 + 32s + -8s3 = 64 + 32s Reorder the terms: 32S + -32s + 32s + 16sS + -16s2 + -8s3 = 64 + 32s Combine like terms: -32s + 32s = 0 32S + 0 + 16sS + -16s2 + -8s3 = 64 + 32s 32S + 16sS + -16s2 + -8s3 = 64 + 32s Add '16s2' to each side of the equation. 32S + 16sS + -16s2 + 16s2 + -8s3 = 64 + 32s + 16s2 Combine like terms: -16s2 + 16s2 = 0 32S + 16sS + 0 + -8s3 = 64 + 32s + 16s2 32S + 16sS + -8s3 = 64 + 32s + 16s2 Add '8s3' to each side of the equation. 32S + 16sS + -8s3 + 8s3 = 64 + 32s + 16s2 + 8s3 Combine like terms: -8s3 + 8s3 = 0 32S + 16sS + 0 = 64 + 32s + 16s2 + 8s3 32S + 16sS = 64 + 32s + 16s2 + 8s3 Reorder the terms: -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 64 + 32s + 16s2 + 8s3 + -64 + -32s + -16s2 + -8s3 Reorder the terms: -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 64 + -64 + 32s + -32s + 16s2 + -16s2 + 8s3 + -8s3 Combine like terms: 64 + -64 = 0 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 32s + -32s + 16s2 + -16s2 + 8s3 + -8s3 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 32s + -32s + 16s2 + -16s2 + 8s3 + -8s3 Combine like terms: 32s + -32s = 0 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 16s2 + -16s2 + 8s3 + -8s3 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 16s2 + -16s2 + 8s3 + -8s3 Combine like terms: 16s2 + -16s2 = 0 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 + 8s3 + -8s3 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 8s3 + -8s3 Combine like terms: 8s3 + -8s3 = 0 -64 + 32S + -32s + 16sS + -16s2 + -8s3 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-8 + 4S + -4s + 2sS + -2s2 + -1s3) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-8 + 4S + -4s + 2sS + -2s2 + -1s3)' equal to zero and attempt to solve: Simplifying -8 + 4S + -4s + 2sS + -2s2 + -1s3 = 0 Solving -8 + 4S + -4s + 2sS + -2s2 + -1s3 = 0 Move all terms containing S to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 4S + -4s + 2sS + -2s2 + 8 + -1s3 = 0 + 8 Reorder the terms: -8 + 8 + 4S + -4s + 2sS + -2s2 + -1s3 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4S + -4s + 2sS + -2s2 + -1s3 = 0 + 8 4S + -4s + 2sS + -2s2 + -1s3 = 0 + 8 Combine like terms: 0 + 8 = 8 4S + -4s + 2sS + -2s2 + -1s3 = 8 Add '4s' to each side of the equation. 4S + -4s + 2sS + -2s2 + 4s + -1s3 = 8 + 4s Reorder the terms: 4S + -4s + 4s + 2sS + -2s2 + -1s3 = 8 + 4s Combine like terms: -4s + 4s = 0 4S + 0 + 2sS + -2s2 + -1s3 = 8 + 4s 4S + 2sS + -2s2 + -1s3 = 8 + 4s Add '2s2' to each side of the equation. 4S + 2sS + -2s2 + 2s2 + -1s3 = 8 + 4s + 2s2 Combine like terms: -2s2 + 2s2 = 0 4S + 2sS + 0 + -1s3 = 8 + 4s + 2s2 4S + 2sS + -1s3 = 8 + 4s + 2s2 Add 's3' to each side of the equation. 4S + 2sS + -1s3 + s3 = 8 + 4s + 2s2 + s3 Combine like terms: -1s3 + s3 = 0 4S + 2sS + 0 = 8 + 4s + 2s2 + s3 4S + 2sS = 8 + 4s + 2s2 + s3 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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