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Simplifying x2 + 10x + -52 = 0 Reorder the terms: -52 + 10x + x2 = 0 Solving -52 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 10x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 10x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 10x + x2 = 0 + 52 10x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 10x + x2 = 52 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 = 52 + 25 Reorder the terms: 25 + 10x + x2 = 52 + 25 Combine like terms: 52 + 25 = 77 25 + 10x + x2 = 77 Factor a perfect square on the left side: (x + 5)(x + 5) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 5) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 5 = 8.774964387 Simplifying x + 5 = 8.774964387 Reorder the terms: 5 + x = 8.774964387 Solving 5 + x = 8.774964387 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 = 8.774964387 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.774964387 + -5 x = 8.774964387 + -5 Combine like terms: 8.774964387 + -5 = 3.774964387 x = 3.774964387 Simplifying x = 3.774964387Subproblem 2
x + 5 = -8.774964387 Simplifying x + 5 = -8.774964387 Reorder the terms: 5 + x = -8.774964387 Solving 5 + x = -8.774964387 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 = -8.774964387 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.774964387 + -5 x = -8.774964387 + -5 Combine like terms: -8.774964387 + -5 = -13.774964387 x = -13.774964387 Simplifying x = -13.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.774964387, -13.774964387}
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