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Simplifying 6x + -3x(x + -1) = 21 Reorder the terms: 6x + -3x(-1 + x) = 21 6x + (-1 * -3x + x * -3x) = 21 6x + (3x + -3x2) = 21 Combine like terms: 6x + 3x = 9x 9x + -3x2 = 21 Solving 9x + -3x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 9x + -3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 3x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -7 + 3x + -1x2 = 0 Solving -7 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -3x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -3x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -3x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x + x2 = 0 + -7 -3x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -3x + x2 = -7 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -7 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + -3x + x2 = -4.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -4.75 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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