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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 = 17.486832981 x = 17.486832981 Simplifying x = 17.486832981Subproblem 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 = -1.486832981 x = -1.486832981 Simplifying x = -1.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.486832981, -1.486832981}
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