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Simplifying x2 + -3x + -236 = 0 Reorder the terms: -236 + -3x + x2 = 0 Solving -236 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '236' to each side of the equation. -236 + -3x + 236 + x2 = 0 + 236 Reorder the terms: -236 + 236 + -3x + x2 = 0 + 236 Combine like terms: -236 + 236 = 0 0 + -3x + x2 = 0 + 236 -3x + x2 = 0 + 236 Combine like terms: 0 + 236 = 236 -3x + x2 = 236 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 = 236 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 236 + 2.25 Combine like terms: 236 + 2.25 = 238.25 2.25 + -3x + x2 = 238.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 238.25 Calculate the square root of the right side: 15.43534904 Break this problem into two subproblems by setting (x + -1.5) equal to 15.43534904 and -15.43534904.Subproblem 1
x + -1.5 = 15.43534904 Simplifying x + -1.5 = 15.43534904 Reorder the terms: -1.5 + x = 15.43534904 Solving -1.5 + x = 15.43534904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 15.43534904 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 15.43534904 + 1.5 x = 15.43534904 + 1.5 Combine like terms: 15.43534904 + 1.5 = 16.93534904 x = 16.93534904 Simplifying x = 16.93534904Subproblem 2
x + -1.5 = -15.43534904 Simplifying x + -1.5 = -15.43534904 Reorder the terms: -1.5 + x = -15.43534904 Solving -1.5 + x = -15.43534904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -15.43534904 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -15.43534904 + 1.5 x = -15.43534904 + 1.5 Combine like terms: -15.43534904 + 1.5 = -13.93534904 x = -13.93534904 Simplifying x = -13.93534904Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.93534904, -13.93534904}
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