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Simplifying 3x + 24 = 2x2 + -7x + 40 Reorder the terms: 24 + 3x = 2x2 + -7x + 40 Reorder the terms: 24 + 3x = 40 + -7x + 2x2 Solving 24 + 3x = 40 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: 24 + -40 + 3x + 7x + -2x2 = 40 + -7x + 2x2 + -40 + 7x + -2x2 Combine like terms: 24 + -40 = -16 -16 + 3x + 7x + -2x2 = 40 + -7x + 2x2 + -40 + 7x + -2x2 Combine like terms: 3x + 7x = 10x -16 + 10x + -2x2 = 40 + -7x + 2x2 + -40 + 7x + -2x2 Reorder the terms: -16 + 10x + -2x2 = 40 + -40 + -7x + 7x + 2x2 + -2x2 Combine like terms: 40 + -40 = 0 -16 + 10x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2 -16 + 10x + -2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -16 + 10x + -2x2 = 0 + 2x2 + -2x2 -16 + 10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + 10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 5x + -1x2 = 0 Solving -8 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x + x2 = 0 + -8 -5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5x + x2 = -8 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -8 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5x + x2 = -1.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -1.75 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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