Question

Consider the equation: x 2 − 6 = 2 − 18 x x 2 −6=2−18xx, squared, minus, 6, equals, 2, minus, 18, x 1) Rewrite the equation by completing the square. Your equation should look like ( x + c ) 2 = d (x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or ( x − c ) 2 = d (x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation?

Answer 1

To complete the square of the equation x² - 6 = 2 - 18x, we rearrange it to x² + 18x - 4 = 0 and complete the square to get (x + 9)² = 85. Solving for x, we find two solutions: x = -9 + √85 and x = -9 - √85.

Step-by-step explanation:

To complete the square for the equation x² - 6 = 2 - 18x, we first want to rearrange the equation and move all terms to one side to achieve a quadratic equation of the form ax² + bx + c = 0. Let's move the terms around:

x² + 18x - 4 = 0

To complete the square, we add and subtract the square of half the coefficient of x, which in this case is (18/2)² = 81, to the equation:

x² + 18x + 81 - 81 - 4 = 0

Now, we can write the left side of the equation as a perfect square:

(x + 9)² - 85 = 0

Adding 85 to both sides gives us:

(x + 9)² = 85

Therefore, (x + c)² = d where c = 9 and d = 85.

To find the solutions to the equation, we take the square root of both sides:

x + 9 = ±√85

Therefore, we have two solutions:

• x = -9 + √85
• x = -9 - √85