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Simplifying x2 + -20x + 100 = 32 Reorder the terms: 100 + -20x + x2 = 32 Solving 100 + -20x + x2 = 32 Solving for variable 'x'. Reorder the terms: 100 + -32 + -20x + x2 = 32 + -32 Combine like terms: 100 + -32 = 68 68 + -20x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 68 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + -20x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + -20x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -20x + x2 = 0 + -68 -20x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 -20x + x2 = -68 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -68 + 100 Reorder the terms: 100 + -20x + x2 = -68 + 100 Combine like terms: -68 + 100 = 32 100 + -20x + x2 = 32 Factor a perfect square on the left side: (x + -10)(x + -10) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -10) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -10 = 5.656854249 Simplifying x + -10 = 5.656854249 Reorder the terms: -10 + x = 5.656854249 Solving -10 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.656854249 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.656854249 + 10 x = 5.656854249 + 10 Combine like terms: 5.656854249 + 10 = 15.656854249 x = 15.656854249 Simplifying x = 15.656854249Subproblem 2
x + -10 = -5.656854249 Simplifying x + -10 = -5.656854249 Reorder the terms: -10 + x = -5.656854249 Solving -10 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.656854249 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.656854249 + 10 x = -5.656854249 + 10 Combine like terms: -5.656854249 + 10 = 4.343145751 x = 4.343145751 Simplifying x = 4.343145751Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.656854249, 4.343145751}
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