Question

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

Answer 1

Answer:

$b=\dfrac{2\pm3\sqrt{2}}{2}$

Step-by-step 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 $ax^2+bx+c=0$

• a = 2
• b = -4
• c = -7

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

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

$\implies x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(-7)} }{2(2)}$

$\implies x=\dfrac{4\pm\sqrt{72}}{4}$

$\implies x=\dfrac{4\pm6\sqrt{2}}{4}$

$\implies x=\dfrac{2\pm3\sqrt{2}}{2}$

Finally, change x back to b:

$b=\dfrac{2\pm3\sqrt{2}}{2}$