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Simplifying (5x2 + -4x + 8) + -1(2x2 + 5x + -4) = 0 Reorder the terms: (8 + -4x + 5x2) + -1(2x2 + 5x + -4) = 0 Remove parenthesis around (8 + -4x + 5x2) 8 + -4x + 5x2 + -1(2x2 + 5x + -4) = 0 Reorder the terms: 8 + -4x + 5x2 + -1(-4 + 5x + 2x2) = 0 8 + -4x + 5x2 + (-4 * -1 + 5x * -1 + 2x2 * -1) = 0 8 + -4x + 5x2 + (4 + -5x + -2x2) = 0 Reorder the terms: 8 + 4 + -4x + -5x + 5x2 + -2x2 = 0 Combine like terms: 8 + 4 = 12 12 + -4x + -5x + 5x2 + -2x2 = 0 Combine like terms: -4x + -5x = -9x 12 + -9x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 12 + -9x + 3x2 = 0 Solving 12 + -9x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -3x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -3x + x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + x2 = 0 Solving 4 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + x2 = 0 + -4 -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + x2 = -4 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 = -4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3x + x2 = -1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -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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