Solve 6x=x^2 - 6.
Could someone give me the steps? Thanks
put it in the form of
ax^2+bx+c=0
then use the quadratic equation.
In google type:
"quadratic equation online"
When you see list of results click on:
Free Online Quadratic Equation Solver.Solve by Quadratic Formula
When page be open in rectacangle type:
6x=x^2-6
and click option solve it
You will see solution step-by-step
To solve the equation 6x = x^2 - 6, we can follow these steps:
Step 1: Rearrange the equation to bring all the terms to one side:
x^2 - 6 - 6x = 0
Step 2: Simplify the equation if possible. In this case, we don't need to make any simplifications.
Step 3: Make sure the equation is in standard quadratic form, which is ax^2 + bx + c = 0. Comparing the given equation to this form, we have a = 1, b = -6, and c = -6.
Step 4: Now, we can use the quadratic formula to find the solutions of the equation. The quadratic formula states that for any equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting in the values for a, b, and c from our equation, we get:
x = (-(-6) ± √((-6)^2 - 4(1)(-6))) / (2(1))
Simplifying further:
x = (6 ± √(36 + 24)) / 2
x = (6 ± √60) / 2
Step 5: Now, we can simplify the expression under the square root:
√60 = √(6 * 10) = √6 * √10 ≈ 2.45 * √10
Step 6: Finally, we can substitute this value back into our equation:
x = (6 ± 2.45 * √10) / 2
Simplifying further:
x = 3 ± 1.225 * √10
So, the two solutions to the equation 6x = x^2 - 6 are:
x = 3 + 1.225 * √10
x = 3 - 1.225 * √10