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Simplifying 6x + -2x(x + -5) = 46 Reorder the terms: 6x + -2x(-5 + x) = 46 6x + (-5 * -2x + x * -2x) = 46 6x + (10x + -2x2) = 46 Combine like terms: 6x + 10x = 16x 16x + -2x2 = 46 Solving 16x + -2x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 16x + -2x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -23 + 8x + -1x2 = 0 Solving -23 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 23 + -8x + x2 = 0 Move the constant term to the right: Add '-23' to each side of the equation. 23 + -8x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -8x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -8x + x2 = 0 + -23 -8x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -8x + x2 = -23 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -23 + 16 Reorder the terms: 16 + -8x + x2 = -23 + 16 Combine like terms: -23 + 16 = -7 16 + -8x + x2 = -7 Factor a perfect square on the left side: (x + -4)(x + -4) = -7 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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