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Simplifying -10 = 4x(x + -1) + 2(3 + -5x) Reorder the terms: -10 = 4x(-1 + x) + 2(3 + -5x) -10 = (-1 * 4x + x * 4x) + 2(3 + -5x) -10 = (-4x + 4x2) + 2(3 + -5x) -10 = -4x + 4x2 + (3 * 2 + -5x * 2) -10 = -4x + 4x2 + (6 + -10x) Reorder the terms: -10 = 6 + -4x + -10x + 4x2 Combine like terms: -4x + -10x = -14x -10 = 6 + -14x + 4x2 Solving -10 = 6 + -14x + 4x2 Solving for variable 'x'. Combine like terms: -10 + -6 = -16 -16 + 14x + -4x2 = 6 + -14x + 4x2 + -6 + 14x + -4x2 Reorder the terms: -16 + 14x + -4x2 = 6 + -6 + -14x + 14x + 4x2 + -4x2 Combine like terms: 6 + -6 = 0 -16 + 14x + -4x2 = 0 + -14x + 14x + 4x2 + -4x2 -16 + 14x + -4x2 = -14x + 14x + 4x2 + -4x2 Combine like terms: -14x + 14x = 0 -16 + 14x + -4x2 = 0 + 4x2 + -4x2 -16 + 14x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -16 + 14x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 7x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 7x + -2x2)' equal to zero and attempt to solve: Simplifying -8 + 7x + -2x2 = 0 Solving -8 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4 + -3.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3.5x + x2 = 0 + -4 -3.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3.5x + x2 = -4 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -4 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -4 + 3.0625 Combine like terms: -4 + 3.0625 = -0.9375 3.0625 + -3.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -0.9375 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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