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Simplifying -9 = 5x2 + x Reorder the terms: -9 = x + 5x2 Solving -9 = x + 5x2 Solving for variable 'x'. Reorder the terms: -9 + -1x + -5x2 = x + -1x + 5x2 + -5x2 Combine like terms: x + -1x = 0 -9 + -1x + -5x2 = 0 + 5x2 + -5x2 -9 + -1x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -9 + -1x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + x + 5x2)' equal to zero and attempt to solve: Simplifying 9 + x + 5x2 = 0 Solving 9 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 0.2x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 0.2x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 0.2x + x2 = 0 + -1.8 0.2x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 0.2x + x2 = -1.8 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. 0.2x + 0.25 + x2 = -1.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = -1.8 + 0.25 Combine like terms: -1.8 + 0.25 = -1.55 0.25 + 0.2x + x2 = -1.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.55 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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