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Simplifying 2x2 + 7x + -190 = 0 Reorder the terms: -190 + 7x + 2x2 = 0 Solving -190 + 7x + 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'. -95 + 3.5x + x2 = 0 Move the constant term to the right: Add '95' to each side of the equation. -95 + 3.5x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 3.5x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 3.5x + x2 = 0 + 95 3.5x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 3.5x + x2 = 95 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 95 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 95 + 3.0625 Combine like terms: 95 + 3.0625 = 98.0625 3.0625 + 3.5x + x2 = 98.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 98.0625 Calculate the square root of the right side: 9.90265116 Break this problem into two subproblems by setting (x + 1.75) equal to 9.90265116 and -9.90265116.Subproblem 1
x + 1.75 = 9.90265116 Simplifying x + 1.75 = 9.90265116 Reorder the terms: 1.75 + x = 9.90265116 Solving 1.75 + x = 9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 9.90265116 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 9.90265116 + -1.75 x = 9.90265116 + -1.75 Combine like terms: 9.90265116 + -1.75 = 8.15265116 x = 8.15265116 Simplifying x = 8.15265116Subproblem 2
x + 1.75 = -9.90265116 Simplifying x + 1.75 = -9.90265116 Reorder the terms: 1.75 + x = -9.90265116 Solving 1.75 + x = -9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -9.90265116 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -9.90265116 + -1.75 x = -9.90265116 + -1.75 Combine like terms: -9.90265116 + -1.75 = -11.65265116 x = -11.65265116 Simplifying x = -11.65265116Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.15265116, -11.65265116}
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