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Simplifying x2 + -60x + 15 = 0 Reorder the terms: 15 + -60x + x2 = 0 Solving 15 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -60x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -60x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -60x + x2 = 0 + -15 -60x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -60x + x2 = -15 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 = -15 + 900 Reorder the terms: 900 + -60x + x2 = -15 + 900 Combine like terms: -15 + 900 = 885 900 + -60x + x2 = 885 Factor a perfect square on the left side: (x + -30)(x + -30) = 885 Calculate the square root of the right side: 29.748949561 Break this problem into two subproblems by setting (x + -30) equal to 29.748949561 and -29.748949561.Subproblem 1
x + -30 = 29.748949561 Simplifying x + -30 = 29.748949561 Reorder the terms: -30 + x = 29.748949561 Solving -30 + x = 29.748949561 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 = 29.748949561 + 30 Combine like terms: -30 + 30 = 0 0 + x = 29.748949561 + 30 x = 29.748949561 + 30 Combine like terms: 29.748949561 + 30 = 59.748949561 x = 59.748949561 Simplifying x = 59.748949561Subproblem 2
x + -30 = -29.748949561 Simplifying x + -30 = -29.748949561 Reorder the terms: -30 + x = -29.748949561 Solving -30 + x = -29.748949561 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 = -29.748949561 + 30 Combine like terms: -30 + 30 = 0 0 + x = -29.748949561 + 30 x = -29.748949561 + 30 Combine like terms: -29.748949561 + 30 = 0.251050439 x = 0.251050439 Simplifying x = 0.251050439Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.748949561, 0.251050439}
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