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Simplifying x2 + 4x + -618 = 0 Reorder the terms: -618 + 4x + x2 = 0 Solving -618 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '618' to each side of the equation. -618 + 4x + 618 + x2 = 0 + 618 Reorder the terms: -618 + 618 + 4x + x2 = 0 + 618 Combine like terms: -618 + 618 = 0 0 + 4x + x2 = 0 + 618 4x + x2 = 0 + 618 Combine like terms: 0 + 618 = 618 4x + x2 = 618 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 = 618 + 4 Reorder the terms: 4 + 4x + x2 = 618 + 4 Combine like terms: 618 + 4 = 622 4 + 4x + x2 = 622 Factor a perfect square on the left side: (x + 2)(x + 2) = 622 Calculate the square root of the right side: 24.939927827 Break this problem into two subproblems by setting (x + 2) equal to 24.939927827 and -24.939927827.Subproblem 1
x + 2 = 24.939927827 Simplifying x + 2 = 24.939927827 Reorder the terms: 2 + x = 24.939927827 Solving 2 + x = 24.939927827 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 = 24.939927827 + -2 Combine like terms: 2 + -2 = 0 0 + x = 24.939927827 + -2 x = 24.939927827 + -2 Combine like terms: 24.939927827 + -2 = 22.939927827 x = 22.939927827 Simplifying x = 22.939927827Subproblem 2
x + 2 = -24.939927827 Simplifying x + 2 = -24.939927827 Reorder the terms: 2 + x = -24.939927827 Solving 2 + x = -24.939927827 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 = -24.939927827 + -2 Combine like terms: 2 + -2 = 0 0 + x = -24.939927827 + -2 x = -24.939927827 + -2 Combine like terms: -24.939927827 + -2 = -26.939927827 x = -26.939927827 Simplifying x = -26.939927827Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.939927827, -26.939927827}
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