Question

Solve the quadratic equation by completing the square. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) 4x2 + 10x − 15 = 0

Answer 1

Answer:

$x=\frac{-5+\sqrt{85}}{4},\:x=\frac{-5-\sqrt{85}}{4}$

Step-by-step explanation:

We are given

$4x^2+10x-15=0$

We can solve for x by completing square

Firstly, we will add both sides by 15

$4x^2+10x-15+15=0+15$

$4x^2+10x=15$

now, we can use formula

$a^2+2ab+b^2 =(a+b)^2$

now, we can factor 10x in 2ab form

$(2x)^2+2\times 2x\times \frac{5}{2} =15$

now, we can add both sides by (5/2)^2

$(2x)^2+2\times 2x\times \frac{5}{2}+(\frac{5}{2})^2 =15+(\frac{5}{2})^2$

so, we get square as

$(2x+\frac{5}{2})^2 =15+(\frac{5}{2})^2$

$(2x+\frac{5}{2})^2 =\frac{85}{4}$

now, we can take sqrt both sides

and we get

$2x+\frac{5}{2}=-\frac{\sqrt{85} }{2} ,2x+\frac{5}{2}=\frac{\sqrt{85} }{2}$

now, we can solve for x

and we get

$x=\frac{-5+\sqrt{85}}{4},\:x=\frac{-5-\sqrt{85}}{4}$