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Simplifying 2x2 + x + -2730 = 0 Reorder the terms: -2730 + x + 2x2 = 0 Solving -2730 + x + 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'. -1365 + 0.5x + x2 = 0 Move the constant term to the right: Add '1365' to each side of the equation. -1365 + 0.5x + 1365 + x2 = 0 + 1365 Reorder the terms: -1365 + 1365 + 0.5x + x2 = 0 + 1365 Combine like terms: -1365 + 1365 = 0 0 + 0.5x + x2 = 0 + 1365 0.5x + x2 = 0 + 1365 Combine like terms: 0 + 1365 = 1365 0.5x + x2 = 1365 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 1365 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 1365 + 0.25 Combine like terms: 1365 + 0.25 = 1365.25 0.25 + 0.5x + x2 = 1365.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1365.25 Calculate the square root of the right side: 36.949289574 Break this problem into two subproblems by setting (x + 0.5) equal to 36.949289574 and -36.949289574.Subproblem 1
x + 0.5 = 36.949289574 Simplifying x + 0.5 = 36.949289574 Reorder the terms: 0.5 + x = 36.949289574 Solving 0.5 + x = 36.949289574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 36.949289574 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 36.949289574 + -0.5 x = 36.949289574 + -0.5 Combine like terms: 36.949289574 + -0.5 = 36.449289574 x = 36.449289574 Simplifying x = 36.449289574Subproblem 2
x + 0.5 = -36.949289574 Simplifying x + 0.5 = -36.949289574 Reorder the terms: 0.5 + x = -36.949289574 Solving 0.5 + x = -36.949289574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -36.949289574 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -36.949289574 + -0.5 x = -36.949289574 + -0.5 Combine like terms: -36.949289574 + -0.5 = -37.449289574 x = -37.449289574 Simplifying x = -37.449289574Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.449289574, -37.449289574}
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