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Simplifying x2 + 8x + -210 = 0 Reorder the terms: -210 + 8x + x2 = 0 Solving -210 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + 8x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 8x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 8x + x2 = 0 + 210 8x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 8x + x2 = 210 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 = 210 + 16 Reorder the terms: 16 + 8x + x2 = 210 + 16 Combine like terms: 210 + 16 = 226 16 + 8x + x2 = 226 Factor a perfect square on the left side: (x + 4)(x + 4) = 226 Calculate the square root of the right side: 15.033296378 Break this problem into two subproblems by setting (x + 4) equal to 15.033296378 and -15.033296378.Subproblem 1
x + 4 = 15.033296378 Simplifying x + 4 = 15.033296378 Reorder the terms: 4 + x = 15.033296378 Solving 4 + x = 15.033296378 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 = 15.033296378 + -4 Combine like terms: 4 + -4 = 0 0 + x = 15.033296378 + -4 x = 15.033296378 + -4 Combine like terms: 15.033296378 + -4 = 11.033296378 x = 11.033296378 Simplifying x = 11.033296378Subproblem 2
x + 4 = -15.033296378 Simplifying x + 4 = -15.033296378 Reorder the terms: 4 + x = -15.033296378 Solving 4 + x = -15.033296378 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 = -15.033296378 + -4 Combine like terms: 4 + -4 = 0 0 + x = -15.033296378 + -4 x = -15.033296378 + -4 Combine like terms: -15.033296378 + -4 = -19.033296378 x = -19.033296378 Simplifying x = -19.033296378Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.033296378, -19.033296378}
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