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Simplifying 6x2 + -30x + 225 = 0 Reorder the terms: 225 + -30x + 6x2 = 0 Solving 225 + -30x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(75 + -10x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(75 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying 75 + -10x + 2x2 = 0 Solving 75 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 37.5 + -5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -5x + x2 = 0 + -37.5 -5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -5x + x2 = -37.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -37.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -37.5 + 6.25 Combine like terms: -37.5 + 6.25 = -31.25 6.25 + -5x + x2 = -31.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -31.25 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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