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Simplifying 3x2 + -9(x2 + 3x) = -50 Reorder the terms: 3x2 + -9(3x + x2) = -50 3x2 + (3x * -9 + x2 * -9) = -50 3x2 + (-27x + -9x2) = -50 Reorder the terms: -27x + 3x2 + -9x2 = -50 Combine like terms: 3x2 + -9x2 = -6x2 -27x + -6x2 = -50 Solving -27x + -6x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + -27x + -6x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -27x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -8.333333333 + 4.5x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 4.5x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 4.5x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 4.5x + x2 = 0 + 8.333333333 4.5x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 4.5x + x2 = 8.333333333 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 8.333333333 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 8.333333333 + 5.0625 Combine like terms: 8.333333333 + 5.0625 = 13.395833333 5.0625 + 4.5x + x2 = 13.395833333 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 13.395833333 Calculate the square root of the right side: 3.660031876 Break this problem into two subproblems by setting (x + 2.25) equal to 3.660031876 and -3.660031876.Subproblem 1
x + 2.25 = 3.660031876 Simplifying x + 2.25 = 3.660031876 Reorder the terms: 2.25 + x = 3.660031876 Solving 2.25 + x = 3.660031876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.660031876 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.660031876 + -2.25 x = 3.660031876 + -2.25 Combine like terms: 3.660031876 + -2.25 = 1.410031876 x = 1.410031876 Simplifying x = 1.410031876Subproblem 2
x + 2.25 = -3.660031876 Simplifying x + 2.25 = -3.660031876 Reorder the terms: 2.25 + x = -3.660031876 Solving 2.25 + x = -3.660031876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.660031876 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.660031876 + -2.25 x = -3.660031876 + -2.25 Combine like terms: -3.660031876 + -2.25 = -5.910031876 x = -5.910031876 Simplifying x = -5.910031876Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.410031876, -5.910031876}
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