Question

How do you solve it with quadratic formula?

Answer 1

Given:

$7(x-5)^2=63$

To make this easier, let's expand the left side of the equation. $(x-5)^2$ is the same as $(x-5)(x-5)$. Let's rewrite it:

$7(x-5)(x-5)=63$

Let's use the FOIL method (First, Outer, Inner, Last) to simplify the binomial of $(x-5)(x-5)$ on the left. We then get:

$7(x^2-10x+25)=63$

Distribute the seven on the left side (which means multiply the seven by everything in the parenthesis) We are left with:

$7x^2-70x+175=63$

Since we must have the equation set to 0 to use the quadratic formula, subtract 63 from both sides:

$7x^2-70x+112=0$

Now, we can use the quadratic formula. The quadratic formula is:

$x=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2(a)}$ and $x=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2(a)}$

Let's identify our a, b and c values:

a: 7

b: -70

c: 112

Plug in your values into the equation:

$x=\frac{70+\sqrt{(-70)^2-4(7)(112)}}{2(7)}$

Simplify the value inside the square root (called the discriminant) and the denominator:

$x=\frac{70+\sqrt{1764}}{14}$

Simplify the square root. The square root of 1764 is 42:

$x=\frac{70+42}{14}$

Simplify the numerator:

$x=\frac{112}{14}$

Simplify:

$x=8$

That's just one answer, lets get the other one.

$x=\frac{70-42}{14}$

Simplify the numerator:

$x=\frac{28}{14}$

Simplify:

$x=2$

Your answers would be:

$x=8$

$x=2$

Answer 2

Tell me the answer is correct