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Simplifying (-3x + 6) + -1(4x2 + -7x + 8) = 0 Reorder the terms: (6 + -3x) + -1(4x2 + -7x + 8) = 0 Remove parenthesis around (6 + -3x) 6 + -3x + -1(4x2 + -7x + 8) = 0 Reorder the terms: 6 + -3x + -1(8 + -7x + 4x2) = 0 6 + -3x + (8 * -1 + -7x * -1 + 4x2 * -1) = 0 6 + -3x + (-8 + 7x + -4x2) = 0 Reorder the terms: 6 + -8 + -3x + 7x + -4x2 = 0 Combine like terms: 6 + -8 = -2 -2 + -3x + 7x + -4x2 = 0 Combine like terms: -3x + 7x = 4x -2 + 4x + -4x2 = 0 Solving -2 + 4x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2x + -2x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + -2x2 = 0 Solving -1 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -1x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1x + x2 = 0 + -0.5 -1x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1x + x2 = -0.5 The x term is -1x. 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. -1x + 0.25 + x2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1x + x2 = -0.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.25 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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