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Simplifying 8x2 + -30x + -191 = 0 Reorder the terms: -191 + -30x + 8x2 = 0 Solving -191 + -30x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -23.875 + -3.75x + x2 = 0 Move the constant term to the right: Add '23.875' to each side of the equation. -23.875 + -3.75x + 23.875 + x2 = 0 + 23.875 Reorder the terms: -23.875 + 23.875 + -3.75x + x2 = 0 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + -3.75x + x2 = 0 + 23.875 -3.75x + x2 = 0 + 23.875 Combine like terms: 0 + 23.875 = 23.875 -3.75x + x2 = 23.875 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 23.875 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 23.875 + 3.515625 Combine like terms: 23.875 + 3.515625 = 27.390625 3.515625 + -3.75x + x2 = 27.390625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 27.390625 Calculate the square root of the right side: 5.233605354 Break this problem into two subproblems by setting (x + -1.875) equal to 5.233605354 and -5.233605354.Subproblem 1
x + -1.875 = 5.233605354 Simplifying x + -1.875 = 5.233605354 Reorder the terms: -1.875 + x = 5.233605354 Solving -1.875 + x = 5.233605354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 5.233605354 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 5.233605354 + 1.875 x = 5.233605354 + 1.875 Combine like terms: 5.233605354 + 1.875 = 7.108605354 x = 7.108605354 Simplifying x = 7.108605354Subproblem 2
x + -1.875 = -5.233605354 Simplifying x + -1.875 = -5.233605354 Reorder the terms: -1.875 + x = -5.233605354 Solving -1.875 + x = -5.233605354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -5.233605354 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -5.233605354 + 1.875 x = -5.233605354 + 1.875 Combine like terms: -5.233605354 + 1.875 = -3.358605354 x = -3.358605354 Simplifying x = -3.358605354Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.108605354, -3.358605354}
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