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Simplifying 10x + -6x2 = 28x + 68 Reorder the terms: 10x + -6x2 = 68 + 28x Solving 10x + -6x2 = 68 + 28x Solving for variable 'x'. Reorder the terms: -68 + 10x + -28x + -6x2 = 68 + 28x + -68 + -28x Combine like terms: 10x + -28x = -18x -68 + -18x + -6x2 = 68 + 28x + -68 + -28x Reorder the terms: -68 + -18x + -6x2 = 68 + -68 + 28x + -28x Combine like terms: 68 + -68 = 0 -68 + -18x + -6x2 = 0 + 28x + -28x -68 + -18x + -6x2 = 28x + -28x Combine like terms: 28x + -28x = 0 -68 + -18x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(34 + 9x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(34 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying 34 + 9x + 3x2 = 0 Solving 34 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 11.33333333 + 3x + x2 = 0 Move the constant term to the right: Add '-11.33333333' to each side of the equation. 11.33333333 + 3x + -11.33333333 + x2 = 0 + -11.33333333 Reorder the terms: 11.33333333 + -11.33333333 + 3x + x2 = 0 + -11.33333333 Combine like terms: 11.33333333 + -11.33333333 = 0.00000000 0.00000000 + 3x + x2 = 0 + -11.33333333 3x + x2 = 0 + -11.33333333 Combine like terms: 0 + -11.33333333 = -11.33333333 3x + x2 = -11.33333333 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 = -11.33333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -11.33333333 + 2.25 Combine like terms: -11.33333333 + 2.25 = -9.08333333 2.25 + 3x + x2 = -9.08333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -9.08333333 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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