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Simplifying x2 + 6x + 9 = 89 Reorder the terms: 9 + 6x + x2 = 89 Solving 9 + 6x + x2 = 89 Solving for variable 'x'. Reorder the terms: 9 + -89 + 6x + x2 = 89 + -89 Combine like terms: 9 + -89 = -80 -80 + 6x + x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -80 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 6x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 6x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 6x + x2 = 0 + 80 6x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 6x + x2 = 80 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 80 + 9 Reorder the terms: 9 + 6x + x2 = 80 + 9 Combine like terms: 80 + 9 = 89 9 + 6x + x2 = 89 Factor a perfect square on the left side: (x + 3)(x + 3) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 3) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 3 = 9.433981132 Simplifying x + 3 = 9.433981132 Reorder the terms: 3 + x = 9.433981132 Solving 3 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 9.433981132 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.433981132 + -3 x = 9.433981132 + -3 Combine like terms: 9.433981132 + -3 = 6.433981132 x = 6.433981132 Simplifying x = 6.433981132Subproblem 2
x + 3 = -9.433981132 Simplifying x + 3 = -9.433981132 Reorder the terms: 3 + x = -9.433981132 Solving 3 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -9.433981132 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.433981132 + -3 x = -9.433981132 + -3 Combine like terms: -9.433981132 + -3 = -12.433981132 x = -12.433981132 Simplifying x = -12.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.433981132, -12.433981132}
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