Question

Which expression gives the solutions of –5 + 2x² = –6x?

Answer 1

`x=\frac{-3(+/-)√(19)} {2}`

Explanation:

we have

`-5+2x^(2) =-6x`

Rewrite

`2x^(2)+6x-5=0`

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`2x^(2)+6x-5=0`

so

`a=2\\b=6\\c=-5`

substitute

`x=\frac{-6(+/-)\sqrt{6^(2)-4(2)(-5)}} {2(2)}`

`x=\frac{-6(+/-)√(76)} {4}`

`x=\frac{-6(+/-)2√(19)} {4}`

simplify

`x=\frac{-3(+/-)√(19)} {2}`

Answer 2

We are given with the expression –5 + 2x² = –6x in which the standard form is 2x² + 6x - 5 = 0 . There are two roots to be identified as expected. Through the quadratic equation, we can identify the a, b and c. Using the equation, the roots are 0.679 and -3.679. The expression is {0.679, -3.679}