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Simplifying x2 + 16x + 9 = 49 Reorder the terms: 9 + 16x + x2 = 49 Solving 9 + 16x + x2 = 49 Solving for variable 'x'. Reorder the terms: 9 + -49 + 16x + x2 = 49 + -49 Combine like terms: 9 + -49 = -40 -40 + 16x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -40 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 16x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 16x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 16x + x2 = 0 + 40 16x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 16x + x2 = 40 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 40 + 64 Reorder the terms: 64 + 16x + x2 = 40 + 64 Combine like terms: 40 + 64 = 104 64 + 16x + x2 = 104 Factor a perfect square on the left side: (x + 8)(x + 8) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 8) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 8 = 10.198039027 Simplifying x + 8 = 10.198039027 Reorder the terms: 8 + x = 10.198039027 Solving 8 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.198039027 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.198039027 + -8 x = 10.198039027 + -8 Combine like terms: 10.198039027 + -8 = 2.198039027 x = 2.198039027 Simplifying x = 2.198039027Subproblem 2
x + 8 = -10.198039027 Simplifying x + 8 = -10.198039027 Reorder the terms: 8 + x = -10.198039027 Solving 8 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.198039027 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.198039027 + -8 x = -10.198039027 + -8 Combine like terms: -10.198039027 + -8 = -18.198039027 x = -18.198039027 Simplifying x = -18.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.198039027, -18.198039027}
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