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Simplifying -1x + 56 = 15x + -2x2 Reorder the terms: 56 + -1x = 15x + -2x2 Solving 56 + -1x = 15x + -2x2 Solving for variable 'x'. Combine like terms: -1x + -15x = -16x 56 + -16x + 2x2 = 15x + -2x2 + -15x + 2x2 Reorder the terms: 56 + -16x + 2x2 = 15x + -15x + -2x2 + 2x2 Combine like terms: 15x + -15x = 0 56 + -16x + 2x2 = 0 + -2x2 + 2x2 56 + -16x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 56 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + -8x + x2)' equal to zero and attempt to solve: Simplifying 28 + -8x + x2 = 0 Solving 28 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -8x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -8x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -8x + x2 = 0 + -28 -8x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -8x + x2 = -28 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -28 + 16 Reorder the terms: 16 + -8x + x2 = -28 + 16 Combine like terms: -28 + 16 = -12 16 + -8x + x2 = -12 Factor a perfect square on the left side: (x + -4)(x + -4) = -12 Can't calculate square root of the right side. 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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