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Simplifying x2 + 60x + -10000 = 0 Reorder the terms: -10000 + 60x + x2 = 0 Solving -10000 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 60x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 60x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 60x + x2 = 0 + 10000 60x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 60x + x2 = 10000 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 = 10000 + 900 Reorder the terms: 900 + 60x + x2 = 10000 + 900 Combine like terms: 10000 + 900 = 10900 900 + 60x + x2 = 10900 Factor a perfect square on the left side: (x + 30)(x + 30) = 10900 Calculate the square root of the right side: 104.403065089 Break this problem into two subproblems by setting (x + 30) equal to 104.403065089 and -104.403065089.Subproblem 1
x + 30 = 104.403065089 Simplifying x + 30 = 104.403065089 Reorder the terms: 30 + x = 104.403065089 Solving 30 + x = 104.403065089 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 = 104.403065089 + -30 Combine like terms: 30 + -30 = 0 0 + x = 104.403065089 + -30 x = 104.403065089 + -30 Combine like terms: 104.403065089 + -30 = 74.403065089 x = 74.403065089 Simplifying x = 74.403065089Subproblem 2
x + 30 = -104.403065089 Simplifying x + 30 = -104.403065089 Reorder the terms: 30 + x = -104.403065089 Solving 30 + x = -104.403065089 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 = -104.403065089 + -30 Combine like terms: 30 + -30 = 0 0 + x = -104.403065089 + -30 x = -104.403065089 + -30 Combine like terms: -104.403065089 + -30 = -134.403065089 x = -134.403065089 Simplifying x = -134.403065089Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.403065089, -134.403065089}
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