Question

Use the quadratic formula to solve. SHOW ALL STEPS FOR FULL CREDIT. Make sure that the final answer has a simplified radical. 2x² -10x +3

Answer 1

Answer:

whats that

Step-by-step explanation:

Answer 2

Answer:

$x=\frac{5+\sqrt{19}}{2}\text{ and } x=\frac{5-\sqrt{19}}{2}$

Step-by-step explanation:

If we have the standard form $ax^2+bx+c$, then we can use the quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

First, let's identify our coefficients. We have $2x^2-10x+3$.

This can be rewritten as $(2)x^2+(-10)x+(3)$.

Therefore, a=2, b=-10, and c=3.

Substitute these values into the quadratic formula. This yields:

$x=\frac{-(-10)\pm\sqrt{(-10)^2-4(2)(3)}}{2(2)}$

From here, simplify. Evaluate the expression under the square root:

$x=\frac{10\pm\sqrt{100-24}}{4}$

Evaluate:

$x=\frac{10\pm\sqrt{76}}{4}$

Note that:

$\sqrt{76}=\sqrt{4\cdot 19}=\sqrt{4}\cdot\sqrt{19}=2\sqrt{19}$

Therefore:

$x=\frac{10\pm2\sqrt{19}}{4}$

We can factor out a 2 from both the numerator and the denominator:

$x=\frac{2(5\pm\sqrt{19})}{2(2)}$

Simplify:

$x=\frac{5\pm\sqrt{19}}{2}$

Therefore, our roots are:

$x=\frac{5+\sqrt{19}}{2}\text{ and } x=\frac{5-\sqrt{19}}{2}$