Question

Solve the following quadratic equation for all values of x in simplest form. 2(x + 5)^2 – 3 = 1​

Answer 1

`x = -5 + √(2)` or
`x = -5 - √(2)`

Explanation:

Step 1: Simplify both sides of the equation.

• 
  `2(x+5)^2 - 3 = 1`
• 
  `2x^2 + 20x + 47 = 1`

Step 2: Subtract 1 from both sides.

• 
  `2x^2 + 20x + 47 - 1 = 1 - 1`

• 
  `2x^2 +20x + 46 = 0`

For this equation: a = 2, b = 20, c = 46

Step 3: Utilize quadratic formula with a = 2, b = 20, c = 46.

• x = (-b ± √(b^2-4ac)/2a

• x = (-20 ± √(20^2 - 4·2·46)/2(2)
• x = (-20 ± √(32)/4
• 
  `x = -5 + √(2)` or
  `x = -5 - √(2)`

Therefore, the answer is
`x = -5 + √(2)` or
`x = -5 - √(2)`.