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Simplifying x2 + 4x + -162 = 0 Reorder the terms: -162 + 4x + x2 = 0 Solving -162 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 4x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + 4x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 4x + x2 = 0 + 162 4x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 4x + x2 = 162 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 162 + 4 Reorder the terms: 4 + 4x + x2 = 162 + 4 Combine like terms: 162 + 4 = 166 4 + 4x + x2 = 166 Factor a perfect square on the left side: (x + 2)(x + 2) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 2) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 2 = 12.884098727 Simplifying x + 2 = 12.884098727 Reorder the terms: 2 + x = 12.884098727 Solving 2 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.884098727 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.884098727 + -2 x = 12.884098727 + -2 Combine like terms: 12.884098727 + -2 = 10.884098727 x = 10.884098727 Simplifying x = 10.884098727Subproblem 2
x + 2 = -12.884098727 Simplifying x + 2 = -12.884098727 Reorder the terms: 2 + x = -12.884098727 Solving 2 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.884098727 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.884098727 + -2 x = -12.884098727 + -2 Combine like terms: -12.884098727 + -2 = -14.884098727 x = -14.884098727 Simplifying x = -14.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.884098727, -14.884098727}
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