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Simplifying 2x2 + 47x + -198 = 0 Reorder the terms: -198 + 47x + 2x2 = 0 Solving -198 + 47x + 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'. -99 + 23.5x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + 23.5x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 23.5x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 23.5x + x2 = 0 + 99 23.5x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 23.5x + x2 = 99 The x term is 23.5x. Take half its coefficient (11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. 23.5x + 138.0625 + x2 = 99 + 138.0625 Reorder the terms: 138.0625 + 23.5x + x2 = 99 + 138.0625 Combine like terms: 99 + 138.0625 = 237.0625 138.0625 + 23.5x + x2 = 237.0625 Factor a perfect square on the left side: (x + 11.75)(x + 11.75) = 237.0625 Calculate the square root of the right side: 15.39683409 Break this problem into two subproblems by setting (x + 11.75) equal to 15.39683409 and -15.39683409.Subproblem 1
x + 11.75 = 15.39683409 Simplifying x + 11.75 = 15.39683409 Reorder the terms: 11.75 + x = 15.39683409 Solving 11.75 + x = 15.39683409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = 15.39683409 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = 15.39683409 + -11.75 x = 15.39683409 + -11.75 Combine like terms: 15.39683409 + -11.75 = 3.64683409 x = 3.64683409 Simplifying x = 3.64683409Subproblem 2
x + 11.75 = -15.39683409 Simplifying x + 11.75 = -15.39683409 Reorder the terms: 11.75 + x = -15.39683409 Solving 11.75 + x = -15.39683409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = -15.39683409 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = -15.39683409 + -11.75 x = -15.39683409 + -11.75 Combine like terms: -15.39683409 + -11.75 = -27.14683409 x = -27.14683409 Simplifying x = -27.14683409Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.64683409, -27.14683409}
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