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Simplifying x * x + 6x = 558 Multiply x * x x2 + 6x = 558 Reorder the terms: 6x + x2 = 558 Solving 6x + x2 = 558 Solving for variable 'x'. Reorder the terms: -558 + 6x + x2 = 558 + -558 Combine like terms: 558 + -558 = 0 -558 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '558' to each side of the equation. -558 + 6x + 558 + x2 = 0 + 558 Reorder the terms: -558 + 558 + 6x + x2 = 0 + 558 Combine like terms: -558 + 558 = 0 0 + 6x + x2 = 0 + 558 6x + x2 = 0 + 558 Combine like terms: 0 + 558 = 558 6x + x2 = 558 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 558 + 9 Reorder the terms: 9 + 6x + x2 = 558 + 9 Combine like terms: 558 + 9 = 567 9 + 6x + x2 = 567 Factor a perfect square on the left side: (x + 3)(x + 3) = 567 Calculate the square root of the right side: 23.8117618 Break this problem into two subproblems by setting (x + 3) equal to 23.8117618 and -23.8117618.Subproblem 1
x + 3 = 23.8117618 Simplifying x + 3 = 23.8117618 Reorder the terms: 3 + x = 23.8117618 Solving 3 + x = 23.8117618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 23.8117618 + -3 Combine like terms: 3 + -3 = 0 0 + x = 23.8117618 + -3 x = 23.8117618 + -3 Combine like terms: 23.8117618 + -3 = 20.8117618 x = 20.8117618 Simplifying x = 20.8117618Subproblem 2
x + 3 = -23.8117618 Simplifying x + 3 = -23.8117618 Reorder the terms: 3 + x = -23.8117618 Solving 3 + x = -23.8117618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -23.8117618 + -3 Combine like terms: 3 + -3 = 0 0 + x = -23.8117618 + -3 x = -23.8117618 + -3 Combine like terms: -23.8117618 + -3 = -26.8117618 x = -26.8117618 Simplifying x = -26.8117618Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.8117618, -26.8117618}
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