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Simplifying x2 + -6x + -55 = -2 Reorder the terms: -55 + -6x + x2 = -2 Solving -55 + -6x + x2 = -2 Solving for variable 'x'. Reorder the terms: -55 + 2 + -6x + x2 = -2 + 2 Combine like terms: -55 + 2 = -53 -53 + -6x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -53 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -6x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -6x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -6x + x2 = 0 + 53 -6x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -6x + x2 = 53 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 = 53 + 9 Reorder the terms: 9 + -6x + x2 = 53 + 9 Combine like terms: 53 + 9 = 62 9 + -6x + x2 = 62 Factor a perfect square on the left side: (x + -3)(x + -3) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -3) equal to 7.874007874 and -7.874007874.Subproblem 1
x + -3 = 7.874007874 Simplifying x + -3 = 7.874007874 Reorder the terms: -3 + x = 7.874007874 Solving -3 + x = 7.874007874 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 = 7.874007874 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.874007874 + 3 x = 7.874007874 + 3 Combine like terms: 7.874007874 + 3 = 10.874007874 x = 10.874007874 Simplifying x = 10.874007874Subproblem 2
x + -3 = -7.874007874 Simplifying x + -3 = -7.874007874 Reorder the terms: -3 + x = -7.874007874 Solving -3 + x = -7.874007874 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 = -7.874007874 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.874007874 + 3 x = -7.874007874 + 3 Combine like terms: -7.874007874 + 3 = -4.874007874 x = -4.874007874 Simplifying x = -4.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.874007874, -4.874007874}
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