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Simplifying 8x2 + -24x + 90 = 0 Reorder the terms: 90 + -24x + 8x2 = 0 Solving 90 + -24x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -12x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -12x + 4x2)' equal to zero and attempt to solve: Simplifying 45 + -12x + 4x2 = 0 Solving 45 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + -3x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + -3x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + -3x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + -3x + x2 = 0 + -11.25 -3x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 -3x + x2 = -11.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -11.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -11.25 + 2.25 Combine like terms: -11.25 + 2.25 = -9 2.25 + -3x + x2 = -9 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -9 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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