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Simplifying x2 + 8x + -272 = 0 Reorder the terms: -272 + 8x + x2 = 0 Solving -272 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '272' to each side of the equation. -272 + 8x + 272 + x2 = 0 + 272 Reorder the terms: -272 + 272 + 8x + x2 = 0 + 272 Combine like terms: -272 + 272 = 0 0 + 8x + x2 = 0 + 272 8x + x2 = 0 + 272 Combine like terms: 0 + 272 = 272 8x + x2 = 272 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 = 272 + 16 Reorder the terms: 16 + 8x + x2 = 272 + 16 Combine like terms: 272 + 16 = 288 16 + 8x + x2 = 288 Factor a perfect square on the left side: (x + 4)(x + 4) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + 4) equal to 16.970562748 and -16.970562748.Subproblem 1
x + 4 = 16.970562748 Simplifying x + 4 = 16.970562748 Reorder the terms: 4 + x = 16.970562748 Solving 4 + x = 16.970562748 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 = 16.970562748 + -4 Combine like terms: 4 + -4 = 0 0 + x = 16.970562748 + -4 x = 16.970562748 + -4 Combine like terms: 16.970562748 + -4 = 12.970562748 x = 12.970562748 Simplifying x = 12.970562748Subproblem 2
x + 4 = -16.970562748 Simplifying x + 4 = -16.970562748 Reorder the terms: 4 + x = -16.970562748 Solving 4 + x = -16.970562748 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 = -16.970562748 + -4 Combine like terms: 4 + -4 = 0 0 + x = -16.970562748 + -4 x = -16.970562748 + -4 Combine like terms: -16.970562748 + -4 = -20.970562748 x = -20.970562748 Simplifying x = -20.970562748Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.970562748, -20.970562748}
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