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Simplifying -12x2 + -72x + 299 = 0 Reorder the terms: 299 + -72x + -12x2 = 0 Solving 299 + -72x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -24.91666667 + 6x + x2 = 0 Move the constant term to the right: Add '24.91666667' to each side of the equation. -24.91666667 + 6x + 24.91666667 + x2 = 0 + 24.91666667 Reorder the terms: -24.91666667 + 24.91666667 + 6x + x2 = 0 + 24.91666667 Combine like terms: -24.91666667 + 24.91666667 = 0.00000000 0.00000000 + 6x + x2 = 0 + 24.91666667 6x + x2 = 0 + 24.91666667 Combine like terms: 0 + 24.91666667 = 24.91666667 6x + x2 = 24.91666667 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 = 24.91666667 + 9 Reorder the terms: 9 + 6x + x2 = 24.91666667 + 9 Combine like terms: 24.91666667 + 9 = 33.91666667 9 + 6x + x2 = 33.91666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 33.91666667 Calculate the square root of the right side: 5.823801737 Break this problem into two subproblems by setting (x + 3) equal to 5.823801737 and -5.823801737.Subproblem 1
x + 3 = 5.823801737 Simplifying x + 3 = 5.823801737 Reorder the terms: 3 + x = 5.823801737 Solving 3 + x = 5.823801737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.823801737 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.823801737 + -3 x = 5.823801737 + -3 Combine like terms: 5.823801737 + -3 = 2.823801737 x = 2.823801737 Simplifying x = 2.823801737Subproblem 2
x + 3 = -5.823801737 Simplifying x + 3 = -5.823801737 Reorder the terms: 3 + x = -5.823801737 Solving 3 + x = -5.823801737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.823801737 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.823801737 + -3 x = -5.823801737 + -3 Combine like terms: -5.823801737 + -3 = -8.823801737 x = -8.823801737 Simplifying x = -8.823801737Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.823801737, -8.823801737}
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