Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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

Sagot :

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].

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.