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Simplifying -2x2 + 18x + -40 = 2x + 10 Reorder the terms: -40 + 18x + -2x2 = 2x + 10 Reorder the terms: -40 + 18x + -2x2 = 10 + 2x Solving -40 + 18x + -2x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: -40 + -10 + 18x + -2x + -2x2 = 10 + 2x + -10 + -2x Combine like terms: -40 + -10 = -50 -50 + 18x + -2x + -2x2 = 10 + 2x + -10 + -2x Combine like terms: 18x + -2x = 16x -50 + 16x + -2x2 = 10 + 2x + -10 + -2x Reorder the terms: -50 + 16x + -2x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 -50 + 16x + -2x2 = 0 + 2x + -2x -50 + 16x + -2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -50 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -25 + 8x + -1x2 = 0 Solving -25 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -8x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -8x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -8x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -8x + x2 = 0 + -25 -8x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -8x + x2 = -25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -25 + 16 Reorder the terms: 16 + -8x + x2 = -25 + 16 Combine like terms: -25 + 16 = -9 16 + -8x + x2 = -9 Factor a perfect square on the left side: (x + -4)(x + -4) = -9 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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