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Simplifying x2 + 4x + -316 = 0 Reorder the terms: -316 + 4x + x2 = 0 Solving -316 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '316' to each side of the equation. -316 + 4x + 316 + x2 = 0 + 316 Reorder the terms: -316 + 316 + 4x + x2 = 0 + 316 Combine like terms: -316 + 316 = 0 0 + 4x + x2 = 0 + 316 4x + x2 = 0 + 316 Combine like terms: 0 + 316 = 316 4x + x2 = 316 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 = 316 + 4 Reorder the terms: 4 + 4x + x2 = 316 + 4 Combine like terms: 316 + 4 = 320 4 + 4x + x2 = 320 Factor a perfect square on the left side: (x + 2)(x + 2) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + 2) equal to 17.88854382 and -17.88854382.Subproblem 1
x + 2 = 17.88854382 Simplifying x + 2 = 17.88854382 Reorder the terms: 2 + x = 17.88854382 Solving 2 + x = 17.88854382 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 = 17.88854382 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.88854382 + -2 x = 17.88854382 + -2 Combine like terms: 17.88854382 + -2 = 15.88854382 x = 15.88854382 Simplifying x = 15.88854382Subproblem 2
x + 2 = -17.88854382 Simplifying x + 2 = -17.88854382 Reorder the terms: 2 + x = -17.88854382 Solving 2 + x = -17.88854382 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 = -17.88854382 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.88854382 + -2 x = -17.88854382 + -2 Combine like terms: -17.88854382 + -2 = -19.88854382 x = -19.88854382 Simplifying x = -19.88854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.88854382, -19.88854382}
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