How do you solve $\sqrt{x + 3} = 2 x + 1$ $sqrt(x + 3) = 2x + 1$ ?

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How do you solve $\sqrt{x + 3} = 2 x + 1$ $sqrt(x + 3) = 2x + 1$ ?

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Answer 1 · 2015-08-10T10:48:14

$x = \frac{- 3 \pm \sqrt{41}}{8}$ $x= (-3+-sqrt(41))/8$

Explanation:

Given $\sqrt{x + 3} = 2 x + 1$ $sqrt(x+3) = 2x+1$

Square both sides:
$XXXX$ $color(white)("XXXX")$ $x + 3 = 4 x^{2} + 4 x + 1$ $x+3 = 4x^2+4x+1$

Subtract $(x + 3)$ $(x+3)$ from both sides (and reverse sides)
$XXXX$ $color(white)("XXXX")$ $4 x^{2} + 3 x - 2 = 0$ $4x^2+3x-2=0$

Using the quadratic formula (see below)
$XXXX$ $color(white)("XXXX")$ $x = \frac{- 3 \pm \sqrt{41}}{8}$ $x= (-3+-sqrt(41))/8$

Quadratic formula:
$XXXX$ $color(white)("XXXX")$ for any quadratic in the general form:
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$
$XXXX$ $color(white)("XXXX")$ the solutions are given by the formula:
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

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How do you solve $\sqrt{x + 3} = 2 x + 1$ $sqrt(x + 3) = 2x + 1$ ?

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Explanation:

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How do you solve sqrt(x + 3) = 2x + 1√x+3=2x+1sqrt(x + 3) = 2x + 1?

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How do you solve $\sqrt{x + 3} = 2 x + 1$ $sqrt(x + 3) = 2x + 1$ ?