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Simplifying 2x2 + 300x + 4725 = 0 Reorder the terms: 4725 + 300x + 2x2 = 0 Solving 4725 + 300x + 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'. 2362.5 + 150x + x2 = 0 Move the constant term to the right: Add '-2362.5' to each side of the equation. 2362.5 + 150x + -2362.5 + x2 = 0 + -2362.5 Reorder the terms: 2362.5 + -2362.5 + 150x + x2 = 0 + -2362.5 Combine like terms: 2362.5 + -2362.5 = 0.0 0.0 + 150x + x2 = 0 + -2362.5 150x + x2 = 0 + -2362.5 Combine like terms: 0 + -2362.5 = -2362.5 150x + x2 = -2362.5 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = -2362.5 + 5625 Reorder the terms: 5625 + 150x + x2 = -2362.5 + 5625 Combine like terms: -2362.5 + 5625 = 3262.5 5625 + 150x + x2 = 3262.5 Factor a perfect square on the left side: (x + 75)(x + 75) = 3262.5 Calculate the square root of the right side: 57.118298294 Break this problem into two subproblems by setting (x + 75) equal to 57.118298294 and -57.118298294.Subproblem 1
x + 75 = 57.118298294 Simplifying x + 75 = 57.118298294 Reorder the terms: 75 + x = 57.118298294 Solving 75 + x = 57.118298294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 57.118298294 + -75 Combine like terms: 75 + -75 = 0 0 + x = 57.118298294 + -75 x = 57.118298294 + -75 Combine like terms: 57.118298294 + -75 = -17.881701706 x = -17.881701706 Simplifying x = -17.881701706Subproblem 2
x + 75 = -57.118298294 Simplifying x + 75 = -57.118298294 Reorder the terms: 75 + x = -57.118298294 Solving 75 + x = -57.118298294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -57.118298294 + -75 Combine like terms: 75 + -75 = 0 0 + x = -57.118298294 + -75 x = -57.118298294 + -75 Combine like terms: -57.118298294 + -75 = -132.118298294 x = -132.118298294 Simplifying x = -132.118298294Solution
The solution to the problem is based on the solutions from the subproblems. x = {-17.881701706, -132.118298294}
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