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Simplifying -3x2 = 3x + 5 Reorder the terms: -3x2 = 5 + 3x Solving -3x2 = 5 + 3x Solving for variable 'x'. Reorder the terms: -5 + -3x + -3x2 = 5 + 3x + -5 + -3x Reorder the terms: -5 + -3x + -3x2 = 5 + -5 + 3x + -3x Combine like terms: 5 + -5 = 0 -5 + -3x + -3x2 = 0 + 3x + -3x -5 + -3x + -3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -5 + -3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 3x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 3x2 = 0 Solving 5 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x + x2 = 0 + -1.666666667 x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 x + x2 = -1.666666667 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. + 0.25 + x2 = -1.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 1.25 + x2 = -1.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.416666667 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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