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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 = 10.062257748 x = 10.062257748 Simplifying x = 10.062257748Subproblem 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 = -6.062257748 x = -6.062257748 Simplifying x = -6.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.062257748, -6.062257748}
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