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Simplifying 2x2 + 5x + -720 = 0 Reorder the terms: -720 + 5x + 2x2 = 0 Solving -720 + 5x + 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'. -360 + 2.5x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + 2.5x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 2.5x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 2.5x + x2 = 0 + 360 2.5x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 2.5x + x2 = 360 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 360 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 360 + 1.5625 Combine like terms: 360 + 1.5625 = 361.5625 1.5625 + 2.5x + x2 = 361.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 361.5625 Calculate the square root of the right side: 19.01479687 Break this problem into two subproblems by setting (x + 1.25) equal to 19.01479687 and -19.01479687.Subproblem 1
x + 1.25 = 19.01479687 Simplifying x + 1.25 = 19.01479687 Reorder the terms: 1.25 + x = 19.01479687 Solving 1.25 + x = 19.01479687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 19.01479687 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 19.01479687 + -1.25 x = 19.01479687 + -1.25 Combine like terms: 19.01479687 + -1.25 = 17.76479687 x = 17.76479687 Simplifying x = 17.76479687Subproblem 2
x + 1.25 = -19.01479687 Simplifying x + 1.25 = -19.01479687 Reorder the terms: 1.25 + x = -19.01479687 Solving 1.25 + x = -19.01479687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -19.01479687 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -19.01479687 + -1.25 x = -19.01479687 + -1.25 Combine like terms: -19.01479687 + -1.25 = -20.26479687 x = -20.26479687 Simplifying x = -20.26479687Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.76479687, -20.26479687}
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