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Simplifying x2 + -60x + -319 = 0 Reorder the terms: -319 + -60x + x2 = 0 Solving -319 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '319' to each side of the equation. -319 + -60x + 319 + x2 = 0 + 319 Reorder the terms: -319 + 319 + -60x + x2 = 0 + 319 Combine like terms: -319 + 319 = 0 0 + -60x + x2 = 0 + 319 -60x + x2 = 0 + 319 Combine like terms: 0 + 319 = 319 -60x + x2 = 319 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 = 319 + 900 Reorder the terms: 900 + -60x + x2 = 319 + 900 Combine like terms: 319 + 900 = 1219 900 + -60x + x2 = 1219 Factor a perfect square on the left side: (x + -30)(x + -30) = 1219 Calculate the square root of the right side: 34.9141805 Break this problem into two subproblems by setting (x + -30) equal to 34.9141805 and -34.9141805.Subproblem 1
x + -30 = 34.9141805 Simplifying x + -30 = 34.9141805 Reorder the terms: -30 + x = 34.9141805 Solving -30 + x = 34.9141805 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 = 34.9141805 + 30 Combine like terms: -30 + 30 = 0 0 + x = 34.9141805 + 30 x = 34.9141805 + 30 Combine like terms: 34.9141805 + 30 = 64.9141805 x = 64.9141805 Simplifying x = 64.9141805Subproblem 2
x + -30 = -34.9141805 Simplifying x + -30 = -34.9141805 Reorder the terms: -30 + x = -34.9141805 Solving -30 + x = -34.9141805 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 = -34.9141805 + 30 Combine like terms: -30 + 30 = 0 0 + x = -34.9141805 + 30 x = -34.9141805 + 30 Combine like terms: -34.9141805 + 30 = -4.9141805 x = -4.9141805 Simplifying x = -4.9141805Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.9141805, -4.9141805}
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