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Simplifying 4x2 + 30x + 60 = 0 Reorder the terms: 60 + 30x + 4x2 = 0 Solving 60 + 30x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying 30 + 15x + 2x2 = 0 Solving 30 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15 + 7.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 7.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 7.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 7.5x + x2 = 0 + -15 7.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 7.5x + x2 = -15 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -15 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -15 + 14.0625 Combine like terms: -15 + 14.0625 = -0.9375 14.0625 + 7.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = -0.9375 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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