a quadrilateral with angles that mesure: 10x-25, 10x, 3x to the second power, and 2x to the second power. solve for x.
Don't the four angles in a quadrilateral add up to 360° ?
so solve
10x-25 + 10x + 3x^2 + 2x = 360
To solve for x in this case, we can use the fact that the sum of the interior angles of a quadrilateral is always equal to 360 degrees.
So, we can set up an equation by adding all the given angles and setting it equal to 360:
(10x - 25) + (10x) + (3x^2) + (2x^2) = 360
Combining like terms and simplifying the equation:
3x^2 + 2x^2 + 10x - 25 + 10x = 360
5x^2 + 20x - 25 = 360
5x^2 + 20x - 385 = 0
Now we can solve this quadratic equation for x. There are different methods to solve it, but I will show you one way to do it using the quadratic formula.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In our case, a = 5, b = 20, and c = -385.
Plugging in these values into the quadratic formula:
x = (-20 +- sqrt(20^2 - 4*5*(-385))) / (2*5)
Simplifying further:
x = (-20 +- sqrt(400 + 7700)) / 10
x = (-20 +- sqrt(8100)) / 10
x = (-20 +- 90) / 10
Now we have two possible solutions for x:
x = (-20 + 90) / 10 = 70 / 10 = 7
x = (-20 - 90) / 10 = -110 / 10 = -11
Therefore, the solutions for x are x = 7 and x = -11.