Question

What is the solution of 4 StartRoot 5 x 66 EndRoot = x 10?.

Answer 1

The formula of Sridharacharya is used. Then the solutions of the equation are 73.19 and -13.19.

What is a quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The equation is given as

$\rm 4\sqrt{5x + 66} = x +10$

Squaring both sides, we have

16(5x + 66) = (x + 10)²

16(5x + 66) = x² + 100 + 20x

On simplifying, we get

x² + 100 + 20x -80x - 1056 = 0

                     x² - 60x - 956 = 0

On solving by formula method, we have

a = 1; b = -60; and c = -965

$\rm x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\\x = \dfrac{-(-60) \pm \sqrt{(-60)^2 - 4*1*(-965)}}{2*1}\\\\\\x = 73.19, \ -13.19$

Thus, the solutions of the equation are 73.19 and -13.19.

More about the quadratic equation link is given below.

brainly.com/question/2263981