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Simplifying 8x2 + -12x + 18 = 0 Reorder the terms: 18 + -12x + 8x2 = 0 Solving 18 + -12x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -6x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -6x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + -6x + 4x2 = 0 Solving 9 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -1.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -1.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -1.5x + x2 = 0 + -2.25 -1.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -1.5x + x2 = -2.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -2.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.25 + 0.5625 Combine like terms: -2.25 + 0.5625 = -1.6875 0.5625 + -1.5x + x2 = -1.6875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.6875 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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