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Simplifying x2 + -60x + -176 = 0 Reorder the terms: -176 + -60x + x2 = 0 Solving -176 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + -60x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + -60x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + -60x + x2 = 0 + 176 -60x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 -60x + x2 = 176 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 = 176 + 900 Reorder the terms: 900 + -60x + x2 = 176 + 900 Combine like terms: 176 + 900 = 1076 900 + -60x + x2 = 1076 Factor a perfect square on the left side: (x + -30)(x + -30) = 1076 Calculate the square root of the right side: 32.802438934 Break this problem into two subproblems by setting (x + -30) equal to 32.802438934 and -32.802438934.Subproblem 1
x + -30 = 32.802438934 Simplifying x + -30 = 32.802438934 Reorder the terms: -30 + x = 32.802438934 Solving -30 + x = 32.802438934 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 = 32.802438934 + 30 Combine like terms: -30 + 30 = 0 0 + x = 32.802438934 + 30 x = 32.802438934 + 30 Combine like terms: 32.802438934 + 30 = 62.802438934 x = 62.802438934 Simplifying x = 62.802438934Subproblem 2
x + -30 = -32.802438934 Simplifying x + -30 = -32.802438934 Reorder the terms: -30 + x = -32.802438934 Solving -30 + x = -32.802438934 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 = -32.802438934 + 30 Combine like terms: -30 + 30 = 0 0 + x = -32.802438934 + 30 x = -32.802438934 + 30 Combine like terms: -32.802438934 + 30 = -2.802438934 x = -2.802438934 Simplifying x = -2.802438934Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.802438934, -2.802438934}
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