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Simplifying 2x2 + 9x + -600 = 0 Reorder the terms: -600 + 9x + 2x2 = 0 Solving -600 + 9x + 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'. -300 + 4.5x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 4.5x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 4.5x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 4.5x + x2 = 0 + 300 4.5x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 4.5x + x2 = 300 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 300 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 300 + 5.0625 Combine like terms: 300 + 5.0625 = 305.0625 5.0625 + 4.5x + x2 = 305.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 305.0625 Calculate the square root of the right side: 17.466038475 Break this problem into two subproblems by setting (x + 2.25) equal to 17.466038475 and -17.466038475.Subproblem 1
x + 2.25 = 17.466038475 Simplifying x + 2.25 = 17.466038475 Reorder the terms: 2.25 + x = 17.466038475 Solving 2.25 + x = 17.466038475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 17.466038475 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 17.466038475 + -2.25 x = 17.466038475 + -2.25 Combine like terms: 17.466038475 + -2.25 = 15.216038475 x = 15.216038475 Simplifying x = 15.216038475Subproblem 2
x + 2.25 = -17.466038475 Simplifying x + 2.25 = -17.466038475 Reorder the terms: 2.25 + x = -17.466038475 Solving 2.25 + x = -17.466038475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -17.466038475 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -17.466038475 + -2.25 x = -17.466038475 + -2.25 Combine like terms: -17.466038475 + -2.25 = -19.716038475 x = -19.716038475 Simplifying x = -19.716038475Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.216038475, -19.716038475}
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