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Simplifying x2 + 16x = 26 Reorder the terms: 16x + x2 = 26 Solving 16x + x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + 16x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 16x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 16x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 16x + x2 = 0 + 26 16x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 16x + x2 = 26 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 = 26 + 64 Reorder the terms: 64 + 16x + x2 = 26 + 64 Combine like terms: 26 + 64 = 90 64 + 16x + x2 = 90 Factor a perfect square on the left side: (x + 8)(x + 8) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 8) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 8 = 9.486832981 Simplifying x + 8 = 9.486832981 Reorder the terms: 8 + x = 9.486832981 Solving 8 + x = 9.486832981 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 = 9.486832981 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.486832981 + -8 x = 9.486832981 + -8 Combine like terms: 9.486832981 + -8 = 1.486832981 x = 1.486832981 Simplifying x = 1.486832981Subproblem 2
x + 8 = -9.486832981 Simplifying x + 8 = -9.486832981 Reorder the terms: 8 + x = -9.486832981 Solving 8 + x = -9.486832981 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 = -9.486832981 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.486832981 + -8 x = -9.486832981 + -8 Combine like terms: -9.486832981 + -8 = -17.486832981 x = -17.486832981 Simplifying x = -17.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.486832981, -17.486832981}
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