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Simplifying x2 + 60x + -896 = 0 Reorder the terms: -896 + 60x + x2 = 0 Solving -896 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '896' to each side of the equation. -896 + 60x + 896 + x2 = 0 + 896 Reorder the terms: -896 + 896 + 60x + x2 = 0 + 896 Combine like terms: -896 + 896 = 0 0 + 60x + x2 = 0 + 896 60x + x2 = 0 + 896 Combine like terms: 0 + 896 = 896 60x + x2 = 896 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 = 896 + 900 Reorder the terms: 900 + 60x + x2 = 896 + 900 Combine like terms: 896 + 900 = 1796 900 + 60x + x2 = 1796 Factor a perfect square on the left side: (x + 30)(x + 30) = 1796 Calculate the square root of the right side: 42.379240201 Break this problem into two subproblems by setting (x + 30) equal to 42.379240201 and -42.379240201.Subproblem 1
x + 30 = 42.379240201 Simplifying x + 30 = 42.379240201 Reorder the terms: 30 + x = 42.379240201 Solving 30 + x = 42.379240201 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 = 42.379240201 + -30 Combine like terms: 30 + -30 = 0 0 + x = 42.379240201 + -30 x = 42.379240201 + -30 Combine like terms: 42.379240201 + -30 = 12.379240201 x = 12.379240201 Simplifying x = 12.379240201Subproblem 2
x + 30 = -42.379240201 Simplifying x + 30 = -42.379240201 Reorder the terms: 30 + x = -42.379240201 Solving 30 + x = -42.379240201 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 = -42.379240201 + -30 Combine like terms: 30 + -30 = 0 0 + x = -42.379240201 + -30 x = -42.379240201 + -30 Combine like terms: -42.379240201 + -30 = -72.379240201 x = -72.379240201 Simplifying x = -72.379240201Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.379240201, -72.379240201}
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