Answer:
[tex]x = -5 + \sqrt{2}[/tex] or [tex]x = -5 - \sqrt{2}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
- [tex]2(x+5)^2 - 3 = 1[/tex]
- [tex]2x^2 + 20x + 47 = 1[/tex]
Step 2: Subtract 1 from both sides.
- [tex]2x^2 + 20x + 47 - 1 = 1 - 1[/tex]
- [tex]2x^2 +20x + 46 = 0[/tex]
For this equation: a = 2, b = 20, c = 46
Step 3: Utilize quadratic formula with a = 2, b = 20, c = 46.
- x = (-20 ± √(20^2 - 4·2·46)/2(2)
- x = (-20 ± √(32)/4
- [tex]x = -5 + \sqrt{2}[/tex] or [tex]x = -5 - \sqrt{2}[/tex]
Therefore, the answer is [tex]x = -5 + \sqrt{2}[/tex] or [tex]x = -5 - \sqrt{2}[/tex].
