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Simplifying 2x2 + -1x + -720 = 0 Reorder the terms: -720 + -1x + 2x2 = 0 Solving -720 + -1x + 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 + -0.5x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + -0.5x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -0.5x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -0.5x + x2 = 0 + 360 -0.5x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -0.5x + x2 = 360 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 360 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 360 + 0.0625 Combine like terms: 360 + 0.0625 = 360.0625 0.0625 + -0.5x + x2 = 360.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 360.0625 Calculate the square root of the right side: 18.975312909 Break this problem into two subproblems by setting (x + -0.25) equal to 18.975312909 and -18.975312909.Subproblem 1
x + -0.25 = 18.975312909 Simplifying x + -0.25 = 18.975312909 Reorder the terms: -0.25 + x = 18.975312909 Solving -0.25 + x = 18.975312909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 18.975312909 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 18.975312909 + 0.25 x = 18.975312909 + 0.25 Combine like terms: 18.975312909 + 0.25 = 19.225312909 x = 19.225312909 Simplifying x = 19.225312909Subproblem 2
x + -0.25 = -18.975312909 Simplifying x + -0.25 = -18.975312909 Reorder the terms: -0.25 + x = -18.975312909 Solving -0.25 + x = -18.975312909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -18.975312909 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -18.975312909 + 0.25 x = -18.975312909 + 0.25 Combine like terms: -18.975312909 + 0.25 = -18.725312909 x = -18.725312909 Simplifying x = -18.725312909Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.225312909, -18.725312909}
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