2b^2-7=4b I need help solving this

Question

asked Feb 4, 2023 166k views

1 Answer

Daniel Zohar · Answer 1 · 2023-02-08T18:53:11+0000

Answer:

$b=(2\pm3√(2))/(2)$

Explanation:

Rearrange so the equation is in the general form of a quadratic equation
ax^2+bx+c=0

$\implies 2b^2-4b-7=0$

Replace b with x (we will change this back at the end, but this is to avoid confusion when using the quadratic formula):

$\implies 2x^2-4x-7=0$

Therefore, comparing the equation with
ax^2+bx+c=0

Use the quadratic formula to solve, inputting the above values:

$x=(-b\pm√(b^2-4ac) )/(2a)$

$\implies x=(-(-4)\pm√((-4)^2-4(2)(-7)) )/(2(2))$

$\implies x=(4\pm√(72))/(4)$

$\implies x=(4\pm6√(2))/(4)$

$\implies x=(2\pm3√(2))/(2)$

Finally, change x back to b:

$b=(2\pm3√(2))/(2)$