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Simplifying -3x(2x + 7) = 5(x + 9) Reorder the terms: -3x(7 + 2x) = 5(x + 9) (7 * -3x + 2x * -3x) = 5(x + 9) (-21x + -6x2) = 5(x + 9) Reorder the terms: -21x + -6x2 = 5(9 + x) -21x + -6x2 = (9 * 5 + x * 5) -21x + -6x2 = (45 + 5x) Solving -21x + -6x2 = 45 + 5x Solving for variable 'x'. Reorder the terms: -45 + -21x + -5x + -6x2 = 45 + 5x + -45 + -5x Combine like terms: -21x + -5x = -26x -45 + -26x + -6x2 = 45 + 5x + -45 + -5x Reorder the terms: -45 + -26x + -6x2 = 45 + -45 + 5x + -5x Combine like terms: 45 + -45 = 0 -45 + -26x + -6x2 = 0 + 5x + -5x -45 + -26x + -6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -45 + -26x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 26x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 26x + 6x2)' equal to zero and attempt to solve: Simplifying 45 + 26x + 6x2 = 0 Solving 45 + 26x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 7.5 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 4.333333333x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 4.333333333x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 4.333333333x + x2 = 0 + -7.5 4.333333333x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 4.333333333x + x2 = -7.5 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = -7.5 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = -7.5 + 4.694444446 Combine like terms: -7.5 + 4.694444446 = -2.805555554 4.694444446 + 4.333333333x + x2 = -2.805555554 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = -2.805555554 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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