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Simplifying x2 + 4x + -41 = 5 Reorder the terms: -41 + 4x + x2 = 5 Solving -41 + 4x + x2 = 5 Solving for variable 'x'. Reorder the terms: -41 + -5 + 4x + x2 = 5 + -5 Combine like terms: -41 + -5 = -46 -46 + 4x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -46 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 4x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 4x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 4x + x2 = 0 + 46 4x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 4x + x2 = 46 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 = 46 + 4 Reorder the terms: 4 + 4x + x2 = 46 + 4 Combine like terms: 46 + 4 = 50 4 + 4x + x2 = 50 Factor a perfect square on the left side: (x + 2)(x + 2) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 2) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 2 = 7.071067812 Simplifying x + 2 = 7.071067812 Reorder the terms: 2 + x = 7.071067812 Solving 2 + x = 7.071067812 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 = 7.071067812 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.071067812 + -2 x = 7.071067812 + -2 Combine like terms: 7.071067812 + -2 = 5.071067812 x = 5.071067812 Simplifying x = 5.071067812Subproblem 2
x + 2 = -7.071067812 Simplifying x + 2 = -7.071067812 Reorder the terms: 2 + x = -7.071067812 Solving 2 + x = -7.071067812 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 = -7.071067812 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.071067812 + -2 x = -7.071067812 + -2 Combine like terms: -7.071067812 + -2 = -9.071067812 x = -9.071067812 Simplifying x = -9.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.071067812, -9.071067812}
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