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Simplifying 2x2 + 7x + -628 = 0 Reorder the terms: -628 + 7x + 2x2 = 0 Solving -628 + 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'. -314 + 3.5x + x2 = 0 Move the constant term to the right: Add '314' to each side of the equation. -314 + 3.5x + 314 + x2 = 0 + 314 Reorder the terms: -314 + 314 + 3.5x + x2 = 0 + 314 Combine like terms: -314 + 314 = 0 0 + 3.5x + x2 = 0 + 314 3.5x + x2 = 0 + 314 Combine like terms: 0 + 314 = 314 3.5x + x2 = 314 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 = 314 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 314 + 3.0625 Combine like terms: 314 + 3.0625 = 317.0625 3.0625 + 3.5x + x2 = 317.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 317.0625 Calculate the square root of the right side: 17.806248903 Break this problem into two subproblems by setting (x + 1.75) equal to 17.806248903 and -17.806248903.Subproblem 1
x + 1.75 = 17.806248903 Simplifying x + 1.75 = 17.806248903 Reorder the terms: 1.75 + x = 17.806248903 Solving 1.75 + x = 17.806248903 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 = 17.806248903 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 17.806248903 + -1.75 x = 17.806248903 + -1.75 Combine like terms: 17.806248903 + -1.75 = 16.056248903 x = 16.056248903 Simplifying x = 16.056248903Subproblem 2
x + 1.75 = -17.806248903 Simplifying x + 1.75 = -17.806248903 Reorder the terms: 1.75 + x = -17.806248903 Solving 1.75 + x = -17.806248903 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 = -17.806248903 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -17.806248903 + -1.75 x = -17.806248903 + -1.75 Combine like terms: -17.806248903 + -1.75 = -19.556248903 x = -19.556248903 Simplifying x = -19.556248903Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.056248903, -19.556248903}
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