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Simplifying -2x(x + -6) + 7 = 35 Reorder the terms: -2x(-6 + x) + 7 = 35 (-6 * -2x + x * -2x) + 7 = 35 (12x + -2x2) + 7 = 35 Reorder the terms: 7 + 12x + -2x2 = 35 Solving 7 + 12x + -2x2 = 35 Solving for variable 'x'. Reorder the terms: 7 + -35 + 12x + -2x2 = 35 + -35 Combine like terms: 7 + -35 = -28 -28 + 12x + -2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -28 + 12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -14 + 6x + -1x2 = 0 Solving -14 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -6x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -6x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -6x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -6x + x2 = 0 + -14 -6x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -6x + x2 = -14 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 = -14 + 9 Reorder the terms: 9 + -6x + x2 = -14 + 9 Combine like terms: -14 + 9 = -5 9 + -6x + x2 = -5 Factor a perfect square on the left side: (x + -3)(x + -3) = -5 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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