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Simplifying x2 + 10x + 21 = 169 Reorder the terms: 21 + 10x + x2 = 169 Solving 21 + 10x + x2 = 169 Solving for variable 'x'. Reorder the terms: 21 + -169 + 10x + x2 = 169 + -169 Combine like terms: 21 + -169 = -148 -148 + 10x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -148 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '148' to each side of the equation. -148 + 10x + 148 + x2 = 0 + 148 Reorder the terms: -148 + 148 + 10x + x2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + 10x + x2 = 0 + 148 10x + x2 = 0 + 148 Combine like terms: 0 + 148 = 148 10x + x2 = 148 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 = 148 + 25 Reorder the terms: 25 + 10x + x2 = 148 + 25 Combine like terms: 148 + 25 = 173 25 + 10x + x2 = 173 Factor a perfect square on the left side: (x + 5)(x + 5) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (x + 5) equal to 13.152946438 and -13.152946438.Subproblem 1
x + 5 = 13.152946438 Simplifying x + 5 = 13.152946438 Reorder the terms: 5 + x = 13.152946438 Solving 5 + x = 13.152946438 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 = 13.152946438 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.152946438 + -5 x = 13.152946438 + -5 Combine like terms: 13.152946438 + -5 = 8.152946438 x = 8.152946438 Simplifying x = 8.152946438Subproblem 2
x + 5 = -13.152946438 Simplifying x + 5 = -13.152946438 Reorder the terms: 5 + x = -13.152946438 Solving 5 + x = -13.152946438 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 = -13.152946438 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.152946438 + -5 x = -13.152946438 + -5 Combine like terms: -13.152946438 + -5 = -18.152946438 x = -18.152946438 Simplifying x = -18.152946438Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.152946438, -18.152946438}
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