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Simplifying 6x2 + 36x + 48 = -14 + -36 Reorder the terms: 48 + 36x + 6x2 = -14 + -36 Combine like terms: -14 + -36 = -50 48 + 36x + 6x2 = -50 Solving 48 + 36x + 6x2 = -50 Solving for variable 'x'. Reorder the terms: 48 + 50 + 36x + 6x2 = -50 + 50 Combine like terms: 48 + 50 = 98 98 + 36x + 6x2 = -50 + 50 Combine like terms: -50 + 50 = 0 98 + 36x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 18x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 18x + 3x2)' equal to zero and attempt to solve: Simplifying 49 + 18x + 3x2 = 0 Solving 49 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.33333333 + 6x + x2 = 0 Move the constant term to the right: Add '-16.33333333' to each side of the equation. 16.33333333 + 6x + -16.33333333 + x2 = 0 + -16.33333333 Reorder the terms: 16.33333333 + -16.33333333 + 6x + x2 = 0 + -16.33333333 Combine like terms: 16.33333333 + -16.33333333 = 0.00000000 0.00000000 + 6x + x2 = 0 + -16.33333333 6x + x2 = 0 + -16.33333333 Combine like terms: 0 + -16.33333333 = -16.33333333 6x + x2 = -16.33333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -16.33333333 + 9 Reorder the terms: 9 + 6x + x2 = -16.33333333 + 9 Combine like terms: -16.33333333 + 9 = -7.33333333 9 + 6x + x2 = -7.33333333 Factor a perfect square on the left side: (x + 3)(x + 3) = -7.33333333 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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