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Simplifying x2 + 60x + -660000 = 0 Reorder the terms: -660000 + 60x + x2 = 0 Solving -660000 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '660000' to each side of the equation. -660000 + 60x + 660000 + x2 = 0 + 660000 Reorder the terms: -660000 + 660000 + 60x + x2 = 0 + 660000 Combine like terms: -660000 + 660000 = 0 0 + 60x + x2 = 0 + 660000 60x + x2 = 0 + 660000 Combine like terms: 0 + 660000 = 660000 60x + x2 = 660000 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 660000 + 900 Reorder the terms: 900 + 60x + x2 = 660000 + 900 Combine like terms: 660000 + 900 = 660900 900 + 60x + x2 = 660900 Factor a perfect square on the left side: (x + 30)(x + 30) = 660900 Calculate the square root of the right side: 812.957563468 Break this problem into two subproblems by setting (x + 30) equal to 812.957563468 and -812.957563468.Subproblem 1
x + 30 = 812.957563468 Simplifying x + 30 = 812.957563468 Reorder the terms: 30 + x = 812.957563468 Solving 30 + x = 812.957563468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 812.957563468 + -30 Combine like terms: 30 + -30 = 0 0 + x = 812.957563468 + -30 x = 812.957563468 + -30 Combine like terms: 812.957563468 + -30 = 782.957563468 x = 782.957563468 Simplifying x = 782.957563468Subproblem 2
x + 30 = -812.957563468 Simplifying x + 30 = -812.957563468 Reorder the terms: 30 + x = -812.957563468 Solving 30 + x = -812.957563468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -812.957563468 + -30 Combine like terms: 30 + -30 = 0 0 + x = -812.957563468 + -30 x = -812.957563468 + -30 Combine like terms: -812.957563468 + -30 = -842.957563468 x = -842.957563468 Simplifying x = -842.957563468Solution
The solution to the problem is based on the solutions from the subproblems. x = {782.957563468, -842.957563468}
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