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Simplifying 5x2 + -9 = -7x2 + 12x + -18 Reorder the terms: -9 + 5x2 = -7x2 + 12x + -18 Reorder the terms: -9 + 5x2 = -18 + 12x + -7x2 Solving -9 + 5x2 = -18 + 12x + -7x2 Solving for variable 'x'. Reorder the terms: -9 + 18 + -12x + 5x2 + 7x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Combine like terms: -9 + 18 = 9 9 + -12x + 5x2 + 7x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Combine like terms: 5x2 + 7x2 = 12x2 9 + -12x + 12x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Reorder the terms: 9 + -12x + 12x2 = -18 + 18 + 12x + -12x + -7x2 + 7x2 Combine like terms: -18 + 18 = 0 9 + -12x + 12x2 = 0 + 12x + -12x + -7x2 + 7x2 9 + -12x + 12x2 = 12x + -12x + -7x2 + 7x2 Combine like terms: 12x + -12x = 0 9 + -12x + 12x2 = 0 + -7x2 + 7x2 9 + -12x + 12x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 9 + -12x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -4x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 4x2 = 0 Solving 3 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -1x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1x + x2 = 0 + -0.75 -1x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1x + x2 = -0.75 The x term is -1x. 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. -1x + 0.25 + x2 = -0.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + -1x + x2 = -0.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.5 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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