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Simplifying -2x2 + 30x + -200 = 0 Reorder the terms: -200 + 30x + -2x2 = 0 Solving -200 + 30x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + 15x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying -100 + 15x + -1x2 = 0 Solving -100 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -15x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -15x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -15x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -15x + x2 = 0 + -100 -15x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -15x + x2 = -100 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -100 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -100 + 56.25 Combine like terms: -100 + 56.25 = -43.75 56.25 + -15x + x2 = -43.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = -43.75 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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