# How do you solve (4x+5)^2=35x+29 using the quadratic formula?

Aug 24, 2016

The Solns. are ${x}_{1} \cong 0.55425 , {x}_{2} \cong - 1.80425$.

#### Explanation:

Formula to find the roots $\alpha , \mathmr{and} \beta$ of the quadr. eqn.

$a {x}^{2} + b x + c + 0$ is, $\alpha , \beta = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Before proceed to solve the given eqn., let us first simplify it :

${\left(4 x + 5\right)}^{2} = 35 x + 29$.

$\Rightarrow 16 {x}^{2} + 40 x + 25 - 35 x - 29 = 0 , i . e . , 4 {x}^{2} + 5 x - 4 = 0$.

So, we have, $a = 4 , b = 5 , c = - 4$

$\therefore \alpha , \beta = \frac{- 5 \pm \sqrt{25 + 64}}{8} = \frac{- 5 \pm \sqrt{89}}{8}$

Taking, #sqrt89~=9.434, we have, the roots

$\alpha \cong 0.55425 , \beta \cong - 1.80425$.

Enjoy Maths.!