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Simplifying (5x2 + -6x + 8) + -1(3x2 + -2x + -4) = 0 Reorder the terms: (8 + -6x + 5x2) + -1(3x2 + -2x + -4) = 0 Remove parenthesis around (8 + -6x + 5x2) 8 + -6x + 5x2 + -1(3x2 + -2x + -4) = 0 Reorder the terms: 8 + -6x + 5x2 + -1(-4 + -2x + 3x2) = 0 8 + -6x + 5x2 + (-4 * -1 + -2x * -1 + 3x2 * -1) = 0 8 + -6x + 5x2 + (4 + 2x + -3x2) = 0 Reorder the terms: 8 + 4 + -6x + 2x + 5x2 + -3x2 = 0 Combine like terms: 8 + 4 = 12 12 + -6x + 2x + 5x2 + -3x2 = 0 Combine like terms: -6x + 2x = -4x 12 + -4x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 12 + -4x + 2x2 = 0 Solving 12 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -2x + x2)' equal to zero and attempt to solve: Simplifying 6 + -2x + x2 = 0 Solving 6 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2x + x2 = 0 + -6 -2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -2x + x2 = -6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -6 + 1 Reorder the terms: 1 + -2x + x2 = -6 + 1 Combine like terms: -6 + 1 = -5 1 + -2x + x2 = -5 Factor a perfect square on the left side: (x + -1)(x + -1) = -5 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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