Question

How would I solve this?

Answer 1

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

$(7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360$

solve for x

Combine like terms

$10x^{2}-70x+180=360$

$10x^{2}-70x-180=0$

Divide by 10 both sides

$x^{2}-7x-18=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$x^{2}-7x-18=0$

so

$a=1\\b=-7\\c=-18$

substitute in the formula

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}$

$x=\frac{7(+/-)\sqrt{121}} {2}$

$x=\frac{7(+/-)11} {2}$

$x=\frac{7(+)11} {2}=9$

$x=\frac{7(-)11} {2}=-2$

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral  is

$24-46x$

substitute the value of x

$24-46(9)=-390\°$

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

$(7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°$

therefore

The valid value of x is x=-2