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Simplifying 5 + 9x + -1x2 = x2 + x + 15 Reorder the terms: 5 + 9x + -1x2 = 15 + x + x2 Solving 5 + 9x + -1x2 = 15 + x + x2 Solving for variable 'x'. Reorder the terms: 5 + -15 + 9x + -1x + -1x2 + -1x2 = 15 + x + x2 + -15 + -1x + -1x2 Combine like terms: 5 + -15 = -10 -10 + 9x + -1x + -1x2 + -1x2 = 15 + x + x2 + -15 + -1x + -1x2 Combine like terms: 9x + -1x = 8x -10 + 8x + -1x2 + -1x2 = 15 + x + x2 + -15 + -1x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 -10 + 8x + -2x2 = 15 + x + x2 + -15 + -1x + -1x2 Reorder the terms: -10 + 8x + -2x2 = 15 + -15 + x + -1x + x2 + -1x2 Combine like terms: 15 + -15 = 0 -10 + 8x + -2x2 = 0 + x + -1x + x2 + -1x2 -10 + 8x + -2x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 -10 + 8x + -2x2 = 0 + x2 + -1x2 -10 + 8x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + -1x2 = 0 Solving -5 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -4x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -4x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x + x2 = 0 + -5 -4x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4x + x2 = -5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -5 + 4 Reorder the terms: 4 + -4x + x2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4x + x2 = -1 Factor a perfect square on the left side: (x + -2)(x + -2) = -1 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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