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Simplifying 0 = 4x2 + -4x + 20 Reorder the terms: 0 = 20 + -4x + 4x2 Solving 0 = 20 + -4x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 4x + -4x2 = 20 + -4x + 4x2 + -20 + 4x + -4x2 Reorder the terms: -20 + 4x + -4x2 = 20 + -20 + -4x + 4x + 4x2 + -4x2 Combine like terms: 20 + -20 = 0 -20 + 4x + -4x2 = 0 + -4x + 4x + 4x2 + -4x2 -20 + 4x + -4x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -20 + 4x + -4x2 = 0 + 4x2 + -4x2 -20 + 4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -20 + 4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + x + -1x2 = 0 Solving -5 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -1x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -1x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x + x2 = 0 + -5 -1x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1x + x2 = -5 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. -1x + 0.25 + x2 = -5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + -1x + x2 = -4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.75 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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