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Simplifying 98 = -2x * 6(2x + 7) Reorder the terms: 98 = -2x * 6(7 + 2x) Reorder the terms for easier multiplication: 98 = -2 * 6x(7 + 2x) Multiply -2 * 6 98 = -12x(7 + 2x) 98 = (7 * -12x + 2x * -12x) 98 = (-84x + -24x2) Solving 98 = -84x + -24x2 Solving for variable 'x'. Reorder the terms: 98 + 84x + 24x2 = -84x + 84x + -24x2 + 24x2 Combine like terms: -84x + 84x = 0 98 + 84x + 24x2 = 0 + -24x2 + 24x2 98 + 84x + 24x2 = -24x2 + 24x2 Combine like terms: -24x2 + 24x2 = 0 98 + 84x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 42x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 42x + 12x2)' equal to zero and attempt to solve: Simplifying 49 + 42x + 12x2 = 0 Solving 49 + 42x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 4.083333333 + 3.5x + x2 = 0 Move the constant term to the right: Add '-4.083333333' to each side of the equation. 4.083333333 + 3.5x + -4.083333333 + x2 = 0 + -4.083333333 Reorder the terms: 4.083333333 + -4.083333333 + 3.5x + x2 = 0 + -4.083333333 Combine like terms: 4.083333333 + -4.083333333 = 0.000000000 0.000000000 + 3.5x + x2 = 0 + -4.083333333 3.5x + x2 = 0 + -4.083333333 Combine like terms: 0 + -4.083333333 = -4.083333333 3.5x + x2 = -4.083333333 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 = -4.083333333 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -4.083333333 + 3.0625 Combine like terms: -4.083333333 + 3.0625 = -1.020833333 3.0625 + 3.5x + x2 = -1.020833333 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -1.020833333 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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