Can you help get started on this equation.
Solve for x.
x^2+52=8x
move the 8x over, then you have a quadratic equation. I think you will get complex roots (real and imaginary).
Just a note: this problem is normally well above the ability of algebra I students.
Of course! I'd be happy to help you get started on solving the equation x^2 + 52 = 8x.
To find the value of x that satisfies this equation, we can use the general method of solving quadratic equations. The goal is to simplify the equation and manipulate it to isolate the variable x on one side of the equation.
Let's go step-by-step:
Step 1: Move all terms to one side of the equation.
x^2 + 52 - 8x = 0
Step 2: Combine like terms.
x^2 - 8x + 52 = 0
Step 3: To solve the quadratic equation, we can use either factoring, completing the square, or the quadratic formula. In this case, factoring does not easily yield integer solutions, so we will use the quadratic formula.
The quadratic formula states:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, the coefficient of x^2 is a = 1, the coefficient of x is b = -8, and the constant term is c = 52.
Step 4: Substitute the values of a, b, and c into the quadratic formula.
x = (-(-8) ± √((-8)^2 - 4(1)(52))) / (2(1))
Step 5: Simplify the equation inside the square root.
x = (8 ± √(64 - 208)) / 2
Step 6: Further simplify.
x = (8 ± √(-144)) / 2
Step 7: Since the square root of a negative number is not a real number, there are no real solutions for x in this equation. Instead, we have complex solutions.
Thus, the equation x^2 + 52 = 8x has no real solutions for x.
I hope this explanation helps you understand how to solve the equation. Let me know if you have any further questions!