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Simplifying x2 + -4x + -312 = 0 Reorder the terms: -312 + -4x + x2 = 0 Solving -312 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + -4x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + -4x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + -4x + x2 = 0 + 312 -4x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 -4x + x2 = 312 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 312 + 4 Reorder the terms: 4 + -4x + x2 = 312 + 4 Combine like terms: 312 + 4 = 316 4 + -4x + x2 = 316 Factor a perfect square on the left side: (x + -2)(x + -2) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (x + -2) equal to 17.776388835 and -17.776388835.Subproblem 1
x + -2 = 17.776388835 Simplifying x + -2 = 17.776388835 Reorder the terms: -2 + x = 17.776388835 Solving -2 + x = 17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 17.776388835 + 2 Combine like terms: -2 + 2 = 0 0 + x = 17.776388835 + 2 x = 17.776388835 + 2 Combine like terms: 17.776388835 + 2 = 19.776388835 x = 19.776388835 Simplifying x = 19.776388835Subproblem 2
x + -2 = -17.776388835 Simplifying x + -2 = -17.776388835 Reorder the terms: -2 + x = -17.776388835 Solving -2 + x = -17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -17.776388835 + 2 Combine like terms: -2 + 2 = 0 0 + x = -17.776388835 + 2 x = -17.776388835 + 2 Combine like terms: -17.776388835 + 2 = -15.776388835 x = -15.776388835 Simplifying x = -15.776388835Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.776388835, -15.776388835}
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