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Simplifying x2 + -8x + -304 = 0 Reorder the terms: -304 + -8x + x2 = 0 Solving -304 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '304' to each side of the equation. -304 + -8x + 304 + x2 = 0 + 304 Reorder the terms: -304 + 304 + -8x + x2 = 0 + 304 Combine like terms: -304 + 304 = 0 0 + -8x + x2 = 0 + 304 -8x + x2 = 0 + 304 Combine like terms: 0 + 304 = 304 -8x + x2 = 304 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 304 + 16 Reorder the terms: 16 + -8x + x2 = 304 + 16 Combine like terms: 304 + 16 = 320 16 + -8x + x2 = 320 Factor a perfect square on the left side: (x + -4)(x + -4) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + -4) equal to 17.88854382 and -17.88854382.Subproblem 1
x + -4 = 17.88854382 Simplifying x + -4 = 17.88854382 Reorder the terms: -4 + x = 17.88854382 Solving -4 + x = 17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 17.88854382 + 4 Combine like terms: -4 + 4 = 0 0 + x = 17.88854382 + 4 x = 17.88854382 + 4 Combine like terms: 17.88854382 + 4 = 21.88854382 x = 21.88854382 Simplifying x = 21.88854382Subproblem 2
x + -4 = -17.88854382 Simplifying x + -4 = -17.88854382 Reorder the terms: -4 + x = -17.88854382 Solving -4 + x = -17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -17.88854382 + 4 Combine like terms: -4 + 4 = 0 0 + x = -17.88854382 + 4 x = -17.88854382 + 4 Combine like terms: -17.88854382 + 4 = -13.88854382 x = -13.88854382 Simplifying x = -13.88854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.88854382, -13.88854382}
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