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Simplifying x2 + 2x + 1 = 90 Reorder the terms: 1 + 2x + x2 = 90 Solving 1 + 2x + x2 = 90 Solving for variable 'x'. Reorder the terms: 1 + -90 + 2x + x2 = 90 + -90 Combine like terms: 1 + -90 = -89 -89 + 2x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -89 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 2x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 2x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 2x + x2 = 0 + 89 2x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 2x + x2 = 89 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 89 + 1 Reorder the terms: 1 + 2x + x2 = 89 + 1 Combine like terms: 89 + 1 = 90 1 + 2x + x2 = 90 Factor a perfect square on the left side: (x + 1)(x + 1) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 1) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 1 = 9.486832981 Simplifying x + 1 = 9.486832981 Reorder the terms: 1 + x = 9.486832981 Solving 1 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.486832981 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.486832981 + -1 x = 9.486832981 + -1 Combine like terms: 9.486832981 + -1 = 8.486832981 x = 8.486832981 Simplifying x = 8.486832981Subproblem 2
x + 1 = -9.486832981 Simplifying x + 1 = -9.486832981 Reorder the terms: 1 + x = -9.486832981 Solving 1 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.486832981 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.486832981 + -1 x = -9.486832981 + -1 Combine like terms: -9.486832981 + -1 = -10.486832981 x = -10.486832981 Simplifying x = -10.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.486832981, -10.486832981}
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