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Simplifying x2 + 84x + -18 = 0 Reorder the terms: -18 + 84x + x2 = 0 Solving -18 + 84x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 84x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 84x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 84x + x2 = 0 + 18 84x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 84x + x2 = 18 The x term is 84x. Take half its coefficient (42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. 84x + 1764 + x2 = 18 + 1764 Reorder the terms: 1764 + 84x + x2 = 18 + 1764 Combine like terms: 18 + 1764 = 1782 1764 + 84x + x2 = 1782 Factor a perfect square on the left side: (x + 42)(x + 42) = 1782 Calculate the square root of the right side: 42.213741838 Break this problem into two subproblems by setting (x + 42) equal to 42.213741838 and -42.213741838.Subproblem 1
x + 42 = 42.213741838 Simplifying x + 42 = 42.213741838 Reorder the terms: 42 + x = 42.213741838 Solving 42 + x = 42.213741838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = 42.213741838 + -42 Combine like terms: 42 + -42 = 0 0 + x = 42.213741838 + -42 x = 42.213741838 + -42 Combine like terms: 42.213741838 + -42 = 0.213741838 x = 0.213741838 Simplifying x = 0.213741838Subproblem 2
x + 42 = -42.213741838 Simplifying x + 42 = -42.213741838 Reorder the terms: 42 + x = -42.213741838 Solving 42 + x = -42.213741838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = -42.213741838 + -42 Combine like terms: 42 + -42 = 0 0 + x = -42.213741838 + -42 x = -42.213741838 + -42 Combine like terms: -42.213741838 + -42 = -84.213741838 x = -84.213741838 Simplifying x = -84.213741838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.213741838, -84.213741838}
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