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Simplifying x2 + 10x + 25 = 69 Reorder the terms: 25 + 10x + x2 = 69 Solving 25 + 10x + x2 = 69 Solving for variable 'x'. Reorder the terms: 25 + -69 + 10x + x2 = 69 + -69 Combine like terms: 25 + -69 = -44 -44 + 10x + x2 = 69 + -69 Combine like terms: 69 + -69 = 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 = 3.306623863 x = 3.306623863 Simplifying x = 3.306623863Subproblem 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 = -13.306623863 x = -13.306623863 Simplifying x = -13.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.306623863, -13.306623863}
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