How do you solve $\sqrt{11 x + 3} - 2 x = 0$ $sqrt( 11x+3) -2x =0$ ?

Question

How do you solve $\sqrt{11 x + 3} - 2 x = 0$ $sqrt( 11x+3) -2x =0$ ?

2 Answers

Impact of this question

3961 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-06T14:50:12

$x = - \frac{1}{4}$ $x=-1/4$ and $x = 3$ $x=3$

Explanation:

$\sqrt{11 x + 3} - 2 x = 0$ $sqrt( 11x+3) -2x =0$

Isolate the radical:

$\sqrt{11 x + 3} = 2 x$ $sqrt( 11x+3)=2x$

${(\sqrt{11 x + 3})}^{2} = {(2 x)}^{2}$ $(sqrt( 11x+3))^2=(2x)^2$

$11 x + 3 = 4 x^{2}$ $11x+3=4x^2$

$0 = 4 x^{2} - 11 x - 3$ $0=4x^2 -11x-3$

Factor:

$(4 x + 1) (x - 3) = 0$ $(4 x + 1) (x - 3) =0$

$x = - \frac{1}{4}$ $x=-1/4$ and $x = 3$ $x=3$

Answer 2 · 2018-06-06T15:04:25

$x = \frac{13 + \sqrt{217}}{8} or \frac{13 - \sqrt{217}}{8}$ $x = (13 + sqrt217)/8 or (13 - sqrt217)/8$

Explanation:

$\sqrt{11 x + 3} - 2 x = 0$ $sqrt(11x + 3) - 2x = 0$

Add $2 x$ $2x$ to both sides;

$\sqrt{11 x + 3} - 2 x + 2 x = 0 + 2 x$ $sqrt(11x + 3) - 2x + 2x = 0 + 2x$

$\sqrt{11 x + 3} = 2 x$ $sqrt(11x+3) = 2x$

Square both sides;

${\sqrt{11 x + 3}}^{2} = {(2 x)}^{2}$ $sqrt(11x + 3)^2 = (2x)^2$

$11 x + 3 = 4 x^{2}$ $11x + 3 = 4x^2$

Rearranging the equation;

$4 x^{2} - 11 x - 3 = 0$ $4x^2 - 11x - 3 = 0$

Using the Quadratic Formula;

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

Where;

$a = 4$ $a= 4$

$b = - 11$ $b= -11$

$c = - 3$ $c =-3$

Substituting the values into the equation..

$x = \frac{- (- 13) \pm \sqrt{{(- 13)}^{2} - 4 (4) (- 3)}}{2 (4)}$ $x = (-(-13) +- sqrt((-13)^2- 4(4)(-3)))/(2(4))$

$x = \frac{13 \pm \sqrt{169 + 48}}{8}$ $x= (13 +- sqrt(169 + 48))/8$

$x = \frac{13 \pm \sqrt{217}}{8}$ $x = (13 +- sqrt217)/8$

$x = \frac{13 + \sqrt{217}}{8} or \frac{13 - \sqrt{217}}{8}$ $x = (13 + sqrt217)/8 or (13 - sqrt217)/8$

Science

Math

Humanities

... and beyond

How do you solve $\sqrt{11 x + 3} - 2 x = 0$ $sqrt( 11x+3) -2x =0$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve √11x+3−2x=0sqrt( 11x+3) -2x =0?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you solve $\sqrt{11 x + 3} - 2 x = 0$ $sqrt( 11x+3) -2x =0$ ?