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Simplifying -2x(x + 3) + 5(x + -2) = x + 1 Reorder the terms: -2x(3 + x) + 5(x + -2) = x + 1 (3 * -2x + x * -2x) + 5(x + -2) = x + 1 (-6x + -2x2) + 5(x + -2) = x + 1 Reorder the terms: -6x + -2x2 + 5(-2 + x) = x + 1 -6x + -2x2 + (-2 * 5 + x * 5) = x + 1 -6x + -2x2 + (-10 + 5x) = x + 1 Reorder the terms: -10 + -6x + 5x + -2x2 = x + 1 Combine like terms: -6x + 5x = -1x -10 + -1x + -2x2 = x + 1 Reorder the terms: -10 + -1x + -2x2 = 1 + x Solving -10 + -1x + -2x2 = 1 + x Solving for variable 'x'. Reorder the terms: -10 + -1 + -1x + -1x + -2x2 = 1 + x + -1 + -1x Combine like terms: -10 + -1 = -11 -11 + -1x + -1x + -2x2 = 1 + x + -1 + -1x Combine like terms: -1x + -1x = -2x -11 + -2x + -2x2 = 1 + x + -1 + -1x Reorder the terms: -11 + -2x + -2x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -11 + -2x + -2x2 = 0 + x + -1x -11 + -2x + -2x2 = x + -1x Combine like terms: x + -1x = 0 -11 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 2x + 2x2 = 0 Solving 11 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x + x2 = 0 + -5.5 x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 x + x2 = -5.5 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 = -5.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -5.5 + 0.25 Combine like terms: -5.5 + 0.25 = -5.25 1.25 + x2 = -5.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -5.25 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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