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Simplifying -300x2 + 10x = 30000 Reorder the terms: 10x + -300x2 = 30000 Solving 10x + -300x2 = 30000 Solving for variable 'x'. Reorder the terms: -30000 + 10x + -300x2 = 30000 + -30000 Combine like terms: 30000 + -30000 = 0 -30000 + 10x + -300x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-3000 + x + -30x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-3000 + x + -30x2)' equal to zero and attempt to solve: Simplifying -3000 + x + -30x2 = 0 Solving -3000 + x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. 100 + -0.03333333333x + x2 = 0.0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -0.03333333333x + -100 + x2 = 0.0 + -100 Reorder the terms: 100 + -100 + -0.03333333333x + x2 = 0.0 + -100 Combine like terms: 100 + -100 = 0 0 + -0.03333333333x + x2 = 0.0 + -100 -0.03333333333x + x2 = 0.0 + -100 Combine like terms: 0.0 + -100 = -100 -0.03333333333x + x2 = -100 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.03333333333x + 0.25 + x2 = -100 + 0.25 Reorder the terms: 0.25 + -0.03333333333x + x2 = -100 + 0.25 Combine like terms: -100 + 0.25 = -99.75 0.25 + -0.03333333333x + x2 = -99.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -99.75 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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