Solve x^2 + (-1/2x + 5)^2 = 25

  • Thread starter Spruance
  • Start date
In summary, the equation x^2 + (-1/2x + 5)^2 = 25 is used to solve for the value of x in a quadratic equation. To solve this equation, you can use the quadratic formula or factor the equation to find the roots. The solutions to this equation are x=4 and x=6. It is possible for this equation to have imaginary solutions if the discriminant (b^2-4ac) is negative. To check if your solutions are correct, you can plug them back into the original equation and see if they satisfy it. This will confirm the accuracy of your solutions.
  • #1
Spruance
33
0
How do we solve this equation:


x^2 + (-1/2x + 5)^2 = 25

Thanks in advance
 
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  • #2
Expand that squared term and you'll see that this quadratic equation simplifies nicely.
 
  • #3
That's assuming that you mean ((-1/2)x + 5)^2 and not (-1/(2x)+ 5)^2.
 
  • #4
Thanks, then

x^2 + (-x/2 + 5)^2 = 25

x2 + x2/4 - 5x + 25 = 25

5x2/4 - 5x = 0 (* 4/5)

x2 - 4x = 0

x(x - 4) = 0

x = 0 or x = 4.
 

1. What is the equation x^2 + (-1/2x + 5)^2 = 25 used for?

The equation x^2 + (-1/2x + 5)^2 = 25 is used to solve for the value of x in a quadratic equation.

2. How do you solve x^2 + (-1/2x + 5)^2 = 25?

To solve x^2 + (-1/2x + 5)^2 = 25, you can use the quadratic formula or factor the equation to find the roots.

3. What are the solutions to x^2 + (-1/2x + 5)^2 = 25?

The solutions to x^2 + (-1/2x + 5)^2 = 25 are x=4 and x=6.

4. Can this equation have imaginary solutions?

Yes, this equation can have imaginary solutions if the discriminant (b^2-4ac) is negative.

5. How can I check if my solutions to x^2 + (-1/2x + 5)^2 = 25 are correct?

You can check your solutions by plugging them back into the original equation and seeing if it satisfies the equation. This will confirm that your solutions are correct.

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