How do you solve $8 x + 1 = 4 x^{2}$ $8x+1=4x^2$ by quadratic formula?

Question

How do you solve $8 x + 1 = 4 x^{2}$ $8x+1=4x^2$ by quadratic formula?

2 Answers

Impact of this question

3639 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-07T08:17:11

$8 x + 1 = 4 x^{2}$ $8x+1=4x^2$

$\to 8 x = 4 x^{2} - 1$ $rarr8x=4x^2-1$

$\to 4 x^{2} - 1 - 8 x = 0$ $rarr4x^2-1-8x=0$

In standard form:

$\to 4 x^{2} - 8 x - 1 = 0$ $rarr4x^2-8x-1=0$

Now this is a Quadratic equation (in form $a x^{2} + b x^{2} + c = 0$ $ax^2+bx^2+c=0$ )

Use Quadratic formula:

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

In this case $a = 4, b = - 8, c = - 1$ $a=4,b=-8,c=-1$

Substitute the values into the formula:

$\to x = \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 (4) (- 1)}}{2 (4)}$ $rarrx=(-(-8)+-sqrt((-8)^2-4(4)(-1)))/(2(4))$

$\to x = \frac{8 \pm \sqrt{64 - (- 16)}}{8}$ $rarrx=(8+-sqrt(64-(-16)))/8$

$\to x = \frac{8 \pm \sqrt{64 + 16}}{8}$ $rarrx=(8+-sqrt(64+16))/8$

$\to x = \frac{8 \pm \sqrt{80}}{8}$ $rarrx=(8+-sqrt(80))/8$

$\to x = \frac{8 \pm \sqrt{16 \cdot 5}}{8}$ $rarrx=(8+-sqrt(16*5))/8$

$\to x = \frac{8 \pm 4 \sqrt{5}}{8}$ $rarrx=(8+-4sqrt5)/8$

$\to x = \frac{2 \pm \sqrt{5}}{2}$ $rarrx=(2+-sqrt5)/2$

Answer 2 · 2016-02-07T08:24:14

$\frac{2 \pm \sqrt{5}}{2}$ $(2+-sqrt(5))/(2)$

Explanation:

quadratic fomula

$a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

$\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b+-sqrt(b^2 -4ac))/(2a)$

so $8 x + 1 = 4 x^{2}$ $8x+1=4x^2$

$\to 4 x^{2} - 8 x - 1 = 0$ $rarr4x^2-8x-1=0$

$\to \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 (4) (- 1)}}{2 (4)}$ $rarr(-(-8)+-sqrt((-8)^2 -4(4)(-1)))/(2(4))$

$\to \frac{8 \pm \sqrt{64 + 16}}{8}$ $rarr(8+-sqrt(64 +16))/(8)$

$\to \frac{8 \pm \sqrt{80}}{8}$ $rarr(8+-sqrt(80))/(8)$

$\to \frac{8 \pm 4 \sqrt{5}}{8}$ $rarr(8+-4sqrt(5))/(8)$

$\to \frac{2 \pm \sqrt{5}}{2}$ $rarr(2+-sqrt(5))/(2)$

Science

Math

Humanities

... and beyond

How do you solve $8 x + 1 = 4 x^{2}$ $8x+1=4x^2$ by quadratic formula?

2 Answers

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 8x+1=4x^28x+1=4x28x+1=4x^2 by quadratic formula?

2 Answers

Explanation:

Related questions

Impact of this question

How do you solve $8 x + 1 = 4 x^{2}$ $8x+1=4x^2$ by quadratic formula?