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Simplifying 0 = 4x2 + 38x + 217 Reorder the terms: 0 = 217 + 38x + 4x2 Solving 0 = 217 + 38x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -217 = -217 -217 + -38x + -4x2 = 217 + 38x + 4x2 + -217 + -38x + -4x2 Reorder the terms: -217 + -38x + -4x2 = 217 + -217 + 38x + -38x + 4x2 + -4x2 Combine like terms: 217 + -217 = 0 -217 + -38x + -4x2 = 0 + 38x + -38x + 4x2 + -4x2 -217 + -38x + -4x2 = 38x + -38x + 4x2 + -4x2 Combine like terms: 38x + -38x = 0 -217 + -38x + -4x2 = 0 + 4x2 + -4x2 -217 + -38x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -217 + -38x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(217 + 38x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(217 + 38x + 4x2)' equal to zero and attempt to solve: Simplifying 217 + 38x + 4x2 = 0 Solving 217 + 38x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 54.25 + 9.5x + x2 = 0 Move the constant term to the right: Add '-54.25' to each side of the equation. 54.25 + 9.5x + -54.25 + x2 = 0 + -54.25 Reorder the terms: 54.25 + -54.25 + 9.5x + x2 = 0 + -54.25 Combine like terms: 54.25 + -54.25 = 0.00 0.00 + 9.5x + x2 = 0 + -54.25 9.5x + x2 = 0 + -54.25 Combine like terms: 0 + -54.25 = -54.25 9.5x + x2 = -54.25 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -54.25 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -54.25 + 22.5625 Combine like terms: -54.25 + 22.5625 = -31.6875 22.5625 + 9.5x + x2 = -31.6875 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = -31.6875 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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