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Simplifying (6x2 + -5x) + -1(4x2 + -3x + -4) = 0 Reorder the terms: (-5x + 6x2) + -1(4x2 + -3x + -4) = 0 Remove parenthesis around (-5x + 6x2) -5x + 6x2 + -1(4x2 + -3x + -4) = 0 Reorder the terms: -5x + 6x2 + -1(-4 + -3x + 4x2) = 0 -5x + 6x2 + (-4 * -1 + -3x * -1 + 4x2 * -1) = 0 -5x + 6x2 + (4 + 3x + -4x2) = 0 Reorder the terms: 4 + -5x + 3x + 6x2 + -4x2 = 0 Combine like terms: -5x + 3x = -2x 4 + -2x + 6x2 + -4x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 4 + -2x + 2x2 = 0 Solving 4 + -2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1x + x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + x2 = 0 Solving 2 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x + x2 = 0 + -2 -1x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x + x2 = -2 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 = -2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -1x + x2 = -1.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -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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