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Simplifying x2 + 10x + 25 = 17 Reorder the terms: 25 + 10x + x2 = 17 Solving 25 + 10x + x2 = 17 Solving for variable 'x'. Reorder the terms: 25 + -17 + 10x + x2 = 17 + -17 Combine like terms: 25 + -17 = 8 8 + 10x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 8 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 10x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 10x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 10x + x2 = 0 + -8 10x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 10x + x2 = -8 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 = -8 + 25 Reorder the terms: 25 + 10x + x2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + 10x + x2 = 17 Factor a perfect square on the left side: (x + 5)(x + 5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 5) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 5 = 4.123105626 Simplifying x + 5 = 4.123105626 Reorder the terms: 5 + x = 4.123105626 Solving 5 + x = 4.123105626 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 = 4.123105626 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.123105626 + -5 x = 4.123105626 + -5 Combine like terms: 4.123105626 + -5 = -0.876894374 x = -0.876894374 Simplifying x = -0.876894374Subproblem 2
x + 5 = -4.123105626 Simplifying x + 5 = -4.123105626 Reorder the terms: 5 + x = -4.123105626 Solving 5 + x = -4.123105626 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 = -4.123105626 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.123105626 + -5 x = -4.123105626 + -5 Combine like terms: -4.123105626 + -5 = -9.123105626 x = -9.123105626 Simplifying x = -9.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.876894374, -9.123105626}
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