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Simplifying 3x2 + 27x + -53 = 0 Reorder the terms: -53 + 27x + 3x2 = 0 Solving -53 + 27x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17.66666667 + 9x + x2 = 0 Move the constant term to the right: Add '17.66666667' to each side of the equation. -17.66666667 + 9x + 17.66666667 + x2 = 0 + 17.66666667 Reorder the terms: -17.66666667 + 17.66666667 + 9x + x2 = 0 + 17.66666667 Combine like terms: -17.66666667 + 17.66666667 = 0.00000000 0.00000000 + 9x + x2 = 0 + 17.66666667 9x + x2 = 0 + 17.66666667 Combine like terms: 0 + 17.66666667 = 17.66666667 9x + x2 = 17.66666667 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 17.66666667 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 17.66666667 + 20.25 Combine like terms: 17.66666667 + 20.25 = 37.91666667 20.25 + 9x + x2 = 37.91666667 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 37.91666667 Calculate the square root of the right side: 6.157651068 Break this problem into two subproblems by setting (x + 4.5) equal to 6.157651068 and -6.157651068.Subproblem 1
x + 4.5 = 6.157651068 Simplifying x + 4.5 = 6.157651068 Reorder the terms: 4.5 + x = 6.157651068 Solving 4.5 + x = 6.157651068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 6.157651068 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.157651068 + -4.5 x = 6.157651068 + -4.5 Combine like terms: 6.157651068 + -4.5 = 1.657651068 x = 1.657651068 Simplifying x = 1.657651068Subproblem 2
x + 4.5 = -6.157651068 Simplifying x + 4.5 = -6.157651068 Reorder the terms: 4.5 + x = -6.157651068 Solving 4.5 + x = -6.157651068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -6.157651068 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.157651068 + -4.5 x = -6.157651068 + -4.5 Combine like terms: -6.157651068 + -4.5 = -10.657651068 x = -10.657651068 Simplifying x = -10.657651068Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.657651068, -10.657651068}
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