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Simplifying 0 = 5x2 + 22x + 85 Reorder the terms: 0 = 85 + 22x + 5x2 Solving 0 = 85 + 22x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -85 = -85 -85 + -22x + -5x2 = 85 + 22x + 5x2 + -85 + -22x + -5x2 Reorder the terms: -85 + -22x + -5x2 = 85 + -85 + 22x + -22x + 5x2 + -5x2 Combine like terms: 85 + -85 = 0 -85 + -22x + -5x2 = 0 + 22x + -22x + 5x2 + -5x2 -85 + -22x + -5x2 = 22x + -22x + 5x2 + -5x2 Combine like terms: 22x + -22x = 0 -85 + -22x + -5x2 = 0 + 5x2 + -5x2 -85 + -22x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -85 + -22x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(85 + 22x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(85 + 22x + 5x2)' equal to zero and attempt to solve: Simplifying 85 + 22x + 5x2 = 0 Solving 85 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 17 + 4.4x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + 4.4x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 4.4x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4.4x + x2 = 0 + -17 4.4x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 4.4x + x2 = -17 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = -17 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -17 + 4.84 Combine like terms: -17 + 4.84 = -12.16 4.84 + 4.4x + x2 = -12.16 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = -12.16 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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