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Simplifying x2 + 4x + -61 = 6 Reorder the terms: -61 + 4x + x2 = 6 Solving -61 + 4x + x2 = 6 Solving for variable 'x'. Reorder the terms: -61 + -6 + 4x + x2 = 6 + -6 Combine like terms: -61 + -6 = -67 -67 + 4x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -67 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 4x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + 4x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 4x + x2 = 0 + 67 4x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 4x + x2 = 67 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 = 67 + 4 Reorder the terms: 4 + 4x + x2 = 67 + 4 Combine like terms: 67 + 4 = 71 4 + 4x + x2 = 71 Factor a perfect square on the left side: (x + 2)(x + 2) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 2) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 2 = 8.426149773 Simplifying x + 2 = 8.426149773 Reorder the terms: 2 + x = 8.426149773 Solving 2 + x = 8.426149773 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 = 8.426149773 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.426149773 + -2 x = 8.426149773 + -2 Combine like terms: 8.426149773 + -2 = 6.426149773 x = 6.426149773 Simplifying x = 6.426149773Subproblem 2
x + 2 = -8.426149773 Simplifying x + 2 = -8.426149773 Reorder the terms: 2 + x = -8.426149773 Solving 2 + x = -8.426149773 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 = -8.426149773 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.426149773 + -2 x = -8.426149773 + -2 Combine like terms: -8.426149773 + -2 = -10.426149773 x = -10.426149773 Simplifying x = -10.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.426149773, -10.426149773}
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