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Simplifying 2x2 + -19x + -98 = 0 Reorder the terms: -98 + -19x + 2x2 = 0 Solving -98 + -19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49 + -9.5x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -9.5x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -9.5x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -9.5x + x2 = 0 + 49 -9.5x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -9.5x + x2 = 49 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 49 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 49 + 22.5625 Combine like terms: 49 + 22.5625 = 71.5625 22.5625 + -9.5x + x2 = 71.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 71.5625 Calculate the square root of the right side: 8.459462158 Break this problem into two subproblems by setting (x + -4.75) equal to 8.459462158 and -8.459462158.Subproblem 1
x + -4.75 = 8.459462158 Simplifying x + -4.75 = 8.459462158 Reorder the terms: -4.75 + x = 8.459462158 Solving -4.75 + x = 8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 8.459462158 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 8.459462158 + 4.75 x = 8.459462158 + 4.75 Combine like terms: 8.459462158 + 4.75 = 13.209462158 x = 13.209462158 Simplifying x = 13.209462158Subproblem 2
x + -4.75 = -8.459462158 Simplifying x + -4.75 = -8.459462158 Reorder the terms: -4.75 + x = -8.459462158 Solving -4.75 + x = -8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -8.459462158 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -8.459462158 + 4.75 x = -8.459462158 + 4.75 Combine like terms: -8.459462158 + 4.75 = -3.709462158 x = -3.709462158 Simplifying x = -3.709462158Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.209462158, -3.709462158}
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