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Simplifying 30x + -45 = 6x2 Reorder the terms: -45 + 30x = 6x2 Solving -45 + 30x = 6x2 Solving for variable 'x'. Combine like terms: 6x2 + -6x2 = 0 -45 + 30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 10x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 10x + -2x2)' equal to zero and attempt to solve: Simplifying -15 + 10x + -2x2 = 0 Solving -15 + 10x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -5x + x2 = 0 + -7.5 -5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -5x + x2 = -7.5 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 = -7.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -7.5 + 6.25 Combine like terms: -7.5 + 6.25 = -1.25 6.25 + -5x + x2 = -1.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -1.25 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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