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Simplifying x2 + 8x + -330 = 0 Reorder the terms: -330 + 8x + x2 = 0 Solving -330 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '330' to each side of the equation. -330 + 8x + 330 + x2 = 0 + 330 Reorder the terms: -330 + 330 + 8x + x2 = 0 + 330 Combine like terms: -330 + 330 = 0 0 + 8x + x2 = 0 + 330 8x + x2 = 0 + 330 Combine like terms: 0 + 330 = 330 8x + x2 = 330 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 = 330 + 16 Reorder the terms: 16 + 8x + x2 = 330 + 16 Combine like terms: 330 + 16 = 346 16 + 8x + x2 = 346 Factor a perfect square on the left side: (x + 4)(x + 4) = 346 Calculate the square root of the right side: 18.601075238 Break this problem into two subproblems by setting (x + 4) equal to 18.601075238 and -18.601075238.Subproblem 1
x + 4 = 18.601075238 Simplifying x + 4 = 18.601075238 Reorder the terms: 4 + x = 18.601075238 Solving 4 + x = 18.601075238 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 = 18.601075238 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.601075238 + -4 x = 18.601075238 + -4 Combine like terms: 18.601075238 + -4 = 14.601075238 x = 14.601075238 Simplifying x = 14.601075238Subproblem 2
x + 4 = -18.601075238 Simplifying x + 4 = -18.601075238 Reorder the terms: 4 + x = -18.601075238 Solving 4 + x = -18.601075238 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 = -18.601075238 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.601075238 + -4 x = -18.601075238 + -4 Combine like terms: -18.601075238 + -4 = -22.601075238 x = -22.601075238 Simplifying x = -22.601075238Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.601075238, -22.601075238}
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