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Simplifying 7 = x2 + x + 8 Reorder the terms: 7 = 8 + x + x2 Solving 7 = 8 + x + x2 Solving for variable 'x'. Combine like terms: 7 + -8 = -1 -1 + -1x + -1x2 = 8 + x + x2 + -8 + -1x + -1x2 Reorder the terms: -1 + -1x + -1x2 = 8 + -8 + x + -1x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -1 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2 -1 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 -1 + -1x + -1x2 = 0 + x2 + -1x2 -1 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + x + x2)' equal to zero and attempt to solve: Simplifying 1 + x + x2 = 0 Solving 1 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x + x2 = 0 + -1 x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x + x2 = -1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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