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Simplifying 96 = x(14 + -4x) 96 = (14 * x + -4x * x) 96 = (14x + -4x2) Solving 96 = 14x + -4x2 Solving for variable 'x'. Reorder the terms: 96 + -14x + 4x2 = 14x + -14x + -4x2 + 4x2 Combine like terms: 14x + -14x = 0 96 + -14x + 4x2 = 0 + -4x2 + 4x2 96 + -14x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 96 + -14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 48 + -7x + 2x2 = 0 Solving 48 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24 + -3.5x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -3.5x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -3.5x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -3.5x + x2 = 0 + -24 -3.5x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -3.5x + x2 = -24 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 = -24 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -24 + 3.0625 Combine like terms: -24 + 3.0625 = -20.9375 3.0625 + -3.5x + x2 = -20.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -20.9375 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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