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Simplifying x2 + 10x + 21 = 841 Reorder the terms: 21 + 10x + x2 = 841 Solving 21 + 10x + x2 = 841 Solving for variable 'x'. Reorder the terms: 21 + -841 + 10x + x2 = 841 + -841 Combine like terms: 21 + -841 = -820 -820 + 10x + x2 = 841 + -841 Combine like terms: 841 + -841 = 0 -820 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '820' to each side of the equation. -820 + 10x + 820 + x2 = 0 + 820 Reorder the terms: -820 + 820 + 10x + x2 = 0 + 820 Combine like terms: -820 + 820 = 0 0 + 10x + x2 = 0 + 820 10x + x2 = 0 + 820 Combine like terms: 0 + 820 = 820 10x + x2 = 820 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 = 820 + 25 Reorder the terms: 25 + 10x + x2 = 820 + 25 Combine like terms: 820 + 25 = 845 25 + 10x + x2 = 845 Factor a perfect square on the left side: (x + 5)(x + 5) = 845 Calculate the square root of the right side: 29.068883707 Break this problem into two subproblems by setting (x + 5) equal to 29.068883707 and -29.068883707.Subproblem 1
x + 5 = 29.068883707 Simplifying x + 5 = 29.068883707 Reorder the terms: 5 + x = 29.068883707 Solving 5 + x = 29.068883707 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 = 29.068883707 + -5 Combine like terms: 5 + -5 = 0 0 + x = 29.068883707 + -5 x = 29.068883707 + -5 Combine like terms: 29.068883707 + -5 = 24.068883707 x = 24.068883707 Simplifying x = 24.068883707Subproblem 2
x + 5 = -29.068883707 Simplifying x + 5 = -29.068883707 Reorder the terms: 5 + x = -29.068883707 Solving 5 + x = -29.068883707 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 = -29.068883707 + -5 Combine like terms: 5 + -5 = 0 0 + x = -29.068883707 + -5 x = -29.068883707 + -5 Combine like terms: -29.068883707 + -5 = -34.068883707 x = -34.068883707 Simplifying x = -34.068883707Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.068883707, -34.068883707}
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