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Simplifying 2x2 + 5x + -3 + x2 + -8x + 15 = x2 + x Reorder the terms: -3 + 15 + 5x + -8x + 2x2 + x2 = x2 + x Combine like terms: -3 + 15 = 12 12 + 5x + -8x + 2x2 + x2 = x2 + x Combine like terms: 5x + -8x = -3x 12 + -3x + 2x2 + x2 = x2 + x Combine like terms: 2x2 + x2 = 3x2 12 + -3x + 3x2 = x2 + x Reorder the terms: 12 + -3x + 3x2 = x + x2 Solving 12 + -3x + 3x2 = x + x2 Solving for variable 'x'. Reorder the terms: 12 + -3x + -1x + 3x2 + -1x2 = x + x2 + -1x + -1x2 Combine like terms: -3x + -1x = -4x 12 + -4x + 3x2 + -1x2 = x + x2 + -1x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 12 + -4x + 2x2 = x + x2 + -1x + -1x2 Reorder the terms: 12 + -4x + 2x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 12 + -4x + 2x2 = 0 + x2 + -1x2 12 + -4x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -2x + x2)' equal to zero and attempt to solve: Simplifying 6 + -2x + x2 = 0 Solving 6 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2x + x2 = 0 + -6 -2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -2x + x2 = -6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -6 + 1 Reorder the terms: 1 + -2x + x2 = -6 + 1 Combine like terms: -6 + 1 = -5 1 + -2x + x2 = -5 Factor a perfect square on the left side: (x + -1)(x + -1) = -5 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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