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Simplifying x2 + 6x + 9 = 0.67 Reorder the terms: 9 + 6x + x2 = 0.67 Solving 9 + 6x + x2 = 0.67 Solving for variable 'x'. Reorder the terms: 9 + -0.67 + 6x + x2 = 0.67 + -0.67 Combine like terms: 9 + -0.67 = 8.33 8.33 + 6x + x2 = 0.67 + -0.67 Combine like terms: 0.67 + -0.67 = 0.00 8.33 + 6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-8.33' to each side of the equation. 8.33 + 6x + -8.33 + x2 = 0.00 + -8.33 Reorder the terms: 8.33 + -8.33 + 6x + x2 = 0.00 + -8.33 Combine like terms: 8.33 + -8.33 = 0.00 0.00 + 6x + x2 = 0.00 + -8.33 6x + x2 = 0.00 + -8.33 Combine like terms: 0.00 + -8.33 = -8.33 6x + x2 = -8.33 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 = -8.33 + 9 Reorder the terms: 9 + 6x + x2 = -8.33 + 9 Combine like terms: -8.33 + 9 = 0.67 9 + 6x + x2 = 0.67 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.67 Calculate the square root of the right side: 0.818535277 Break this problem into two subproblems by setting (x + 3) equal to 0.818535277 and -0.818535277.Subproblem 1
x + 3 = 0.818535277 Simplifying x + 3 = 0.818535277 Reorder the terms: 3 + x = 0.818535277 Solving 3 + x = 0.818535277 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 = 0.818535277 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.818535277 + -3 x = 0.818535277 + -3 Combine like terms: 0.818535277 + -3 = -2.181464723 x = -2.181464723 Simplifying x = -2.181464723Subproblem 2
x + 3 = -0.818535277 Simplifying x + 3 = -0.818535277 Reorder the terms: 3 + x = -0.818535277 Solving 3 + x = -0.818535277 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 = -0.818535277 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.818535277 + -3 x = -0.818535277 + -3 Combine like terms: -0.818535277 + -3 = -3.818535277 x = -3.818535277 Simplifying x = -3.818535277Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.181464723, -3.818535277}
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