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Simplifying x2 + 4x + -61 = 0 Reorder the terms: -61 + 4x + x2 = 0 Solving -61 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 4x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 4x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 4x + x2 = 0 + 61 4x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 4x + x2 = 61 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 = 61 + 4 Reorder the terms: 4 + 4x + x2 = 61 + 4 Combine like terms: 61 + 4 = 65 4 + 4x + x2 = 65 Factor a perfect square on the left side: (x + 2)(x + 2) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 2) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 2 = 8.062257748 Simplifying x + 2 = 8.062257748 Reorder the terms: 2 + x = 8.062257748 Solving 2 + x = 8.062257748 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 = 8.062257748 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.062257748 + -2 x = 8.062257748 + -2 Combine like terms: 8.062257748 + -2 = 6.062257748 x = 6.062257748 Simplifying x = 6.062257748Subproblem 2
x + 2 = -8.062257748 Simplifying x + 2 = -8.062257748 Reorder the terms: 2 + x = -8.062257748 Solving 2 + x = -8.062257748 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 = -8.062257748 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.062257748 + -2 x = -8.062257748 + -2 Combine like terms: -8.062257748 + -2 = -10.062257748 x = -10.062257748 Simplifying x = -10.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.062257748, -10.062257748}
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