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Simplifying x * x + 2 + x * 10 = 56 Multiply x * x x2 + 2 + x * 10 = 56 Reorder the terms for easier multiplication: x2 + 2 + 10x = 56 Reorder the terms: 2 + 10x + x2 = 56 Solving 2 + 10x + x2 = 56 Solving for variable 'x'. Reorder the terms: 2 + -56 + 10x + x2 = 56 + -56 Combine like terms: 2 + -56 = -54 -54 + 10x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -54 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 10x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 10x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 10x + x2 = 0 + 54 10x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 10x + x2 = 54 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 = 54 + 25 Reorder the terms: 25 + 10x + x2 = 54 + 25 Combine like terms: 54 + 25 = 79 25 + 10x + x2 = 79 Factor a perfect square on the left side: (x + 5)(x + 5) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 5) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 5 = 8.888194417 Simplifying x + 5 = 8.888194417 Reorder the terms: 5 + x = 8.888194417 Solving 5 + x = 8.888194417 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 = 8.888194417 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.888194417 + -5 x = 8.888194417 + -5 Combine like terms: 8.888194417 + -5 = 3.888194417 x = 3.888194417 Simplifying x = 3.888194417Subproblem 2
x + 5 = -8.888194417 Simplifying x + 5 = -8.888194417 Reorder the terms: 5 + x = -8.888194417 Solving 5 + x = -8.888194417 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 = -8.888194417 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.888194417 + -5 x = -8.888194417 + -5 Combine like terms: -8.888194417 + -5 = -13.888194417 x = -13.888194417 Simplifying x = -13.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.888194417, -13.888194417}
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