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Simplifying x2 + -10x + -50 = -6 Reorder the terms: -50 + -10x + x2 = -6 Solving -50 + -10x + x2 = -6 Solving for variable 'x'. Reorder the terms: -50 + 6 + -10x + x2 = -6 + 6 Combine like terms: -50 + 6 = -44 -44 + -10x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -44 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -10x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -10x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -10x + x2 = 0 + 44 -10x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -10x + x2 = 44 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 44 + 25 Reorder the terms: 25 + -10x + x2 = 44 + 25 Combine like terms: 44 + 25 = 69 25 + -10x + x2 = 69 Factor a perfect square on the left side: (x + -5)(x + -5) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -5) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -5 = 8.306623863 Simplifying x + -5 = 8.306623863 Reorder the terms: -5 + x = 8.306623863 Solving -5 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 8.306623863 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.306623863 + 5 x = 8.306623863 + 5 Combine like terms: 8.306623863 + 5 = 13.306623863 x = 13.306623863 Simplifying x = 13.306623863Subproblem 2
x + -5 = -8.306623863 Simplifying x + -5 = -8.306623863 Reorder the terms: -5 + x = -8.306623863 Solving -5 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -8.306623863 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.306623863 + 5 x = -8.306623863 + 5 Combine like terms: -8.306623863 + 5 = -3.306623863 x = -3.306623863 Simplifying x = -3.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.306623863, -3.306623863}
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