Question

5d^2-145d-600 how to solve this equation

Answer 1

Step-by-step explanation:

$5 {d}^{2} - 145d - 60$

we have this to solve

it's a quadratic equation and 5 is common in whole equation take it out

$5( {d}^{2} - 29d - 12)$

So actually we have to solve d^2-29d-12

Use quadratic formula here,

which is for one root is

$( - b + \sqrt{d} ) \div 2a$

where ax^2+bx+c is quadratic equation.

and d= b^2-4ac,

now a=1, b=-29, c=-12 in d^2-29d-12

firstly let's find d

$d = {b}^{2} - 4ac \\ d = 29 \times 29 - 4 \times 1 \times - 12 \\ d = 841 + 48 \\ d = 889$

but put this in quadratic formula

$first \: root \: = ( - b + \sqrt{d} ) \div 2a \\ = (29 + \sqrt{889} ) \div 2$

now root 889 is almost 29.81 so your roots will be 58.81/2=29.405

similarly other root will be

$second \: root \: = ( - b - \sqrt{d}) \div 2a \\ = (29 - 29.81) \div 2 \\ = - 0.81 \div 2 \\ = - 0.405$

your solution will be

(x-a) (x-b) where a and b are roots

put the value of a and b

$(x - 29.405)(x - ( - 0.405)) \\ = (x - 29.405)(x + 0.405)$

HOPE IT HELPS