Place the steps in the correct order to solve the following equation using the quadratic formula: x^2 - 6x = 10

Answer 1

To solve the equation $x^2-6x=10$ using the quadratic formula, follow these steps in order:

1. Rearrange the equation to standard form: Move all terms to one side of the equation so that it is in the form $a{x}^2+bx+c=0$. $$x^2-6x-10=0$$

2. Identify coefficients: From the standard form $a{x}^2+bx+c=0$, identify the coefficients:

   • $a=1$
   • $b=-6$
   • $c=-10$

3. Use the quadratic formula: The quadratic formula is given by: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ Substitute $a$, $b$, and $c$ into the formula.

4. Calculate the discriminant: Calculate $b^2-4ac$: $$(-6{)}^2-4(1)(-10)=36+40=76$$

5. Calculate the roots using the square root of the discriminant: Now substitute back into the quadratic formula: $$x=\frac{-(-6)\pm \sqrt{76}}{2\cdot 1}$$ Simplifying further: $$x=\frac{6\pm \sqrt{76}}{2}$$

6. Simplify further if necessary: Since $\sqrt{76}$ can be simplified to $2\sqrt{19}$: $$x=\frac{6\pm 2\sqrt{19}}{2}$$ Simplifying gives: $$x=3\pm \sqrt{19}$$

7. Write down the final answers: The solutions are: $$x=3+\sqrt{19}\text{and}x=3-\sqrt{19}$$

So the correct order of steps to solve the equation $x^2-6x=10$ using the quadratic formula is as follows:

1. Rearrange the equation to standard form.
2. Identify coefficients.
3. Use the quadratic formula.
4. Calculate the discriminant.
5. Calculate the roots using the square root of the discriminant.
6. Simplify further if necessary.
7. Write down the final answers.