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

Sagot :

renknee

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 = (-b ± √(b^2-4ac)/2a
  • 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].

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