Solve for x square root of 2x+3=x

$\sqrt{2 x + 3} = x$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 x + 3}}^{2} = x^{2}$

Simplify each side of the equation.

Tap for more steps…

Multiply the exponents in ${({(2 x + 3)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps…

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x + 3)}^{\frac{1}{2} \cdot 2} = x^{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

${(2 x + 3)}^{\frac{1}{2} \cdot 2} = x^{2}$

Rewrite the expression.

${(2 x + 3)}^{1} = x^{2}$

Simplify.

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

Solve for $x$ .

Tap for more steps…

Subtract $x^{2}$ from both sides of the equation.

$2 x + 3 - x^{2} = 0$

Factor the left side of the equation.

Tap for more steps…

Factor $- 1$ out of $2 x + 3 - x^{2}$ .

Tap for more steps…

Reorder the expression.

Tap for more steps…

Move $3$ .

$2 x - x^{2} + 3 = 0$

Reorder $2 x$ and $- x^{2}$ .

$- x^{2} + 2 x + 3 = 0$

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 2 x + 3 = 0$

Factor $- 1$ out of $2 x$ .

$- (x^{2}) - (- 2 x) + 3 = 0$

Rewrite $3$ as $- 1 (- 3)$ .

$- (x^{2}) - (- 2 x) - 1 \cdot - 3 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 2 x)$ .

$- (x^{2} - 2 x) - 1 \cdot - 3 = 0$

Factor $- 1$ out of $- (x^{2} - 2 x) - 1 (- 3)$ .

$- (x^{2} - 2 x - 3) = 0$

Factor.

Tap for more steps…

Factor $x^{2} - 2 x - 3$ using the AC method.

Tap for more steps…

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Multiply each term in $- (x - 3) (x + 1) = 0$ by $- 1$

Tap for more steps…

Multiply each term in $- (x - 3) (x + 1) = 0$ by $- 1$ .

$(- (x - 3) (x + 1)) \cdot - 1 = 0 \cdot - 1$

Simplify $(- (x - 3) (x + 1)) \cdot - 1$ .

Tap for more steps…

Simplify by multiplying through.

Tap for more steps…

Apply the distributive property.

$(- x - - 3) (x + 1) \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $- 3$ .

$(- x + 3) (x + 1) \cdot - 1 = 0 \cdot - 1$

Expand $(- x + 3) (x + 1)$ using the FOIL Method.

Tap for more steps…

Apply the distributive property.

$(- x (x + 1) + 3 (x + 1)) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$(- x \cdot x - x \cdot 1 + 3 (x + 1)) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$(- x \cdot x - x \cdot 1 + 3 x + 3 \cdot 1) \cdot - 1 = 0 \cdot - 1$

Simplify and combine like terms.

Tap for more steps…

Simplify each term.

Tap for more steps…

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps…

Move $x$ .

$(- (x \cdot x) - x \cdot 1 + 3 x + 3 \cdot 1) \cdot - 1 = 0 \cdot - 1$

Multiply $x$ by $x$ .

$(- x^{2} - x \cdot 1 + 3 x + 3 \cdot 1) \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $1$ .

$(- x^{2} - x + 3 x + 3 \cdot 1) \cdot - 1 = 0 \cdot - 1$

Multiply $3$ by $1$ .

$(- x^{2} - x + 3 x + 3) \cdot - 1 = 0 \cdot - 1$

Add $- x$ and $3 x$ .

$(- x^{2} + 2 x + 3) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$- x^{2} \cdot - 1 + 2 x \cdot - 1 + 3 \cdot - 1 = 0 \cdot - 1$

Simplify.

Tap for more steps…

Multiply $- x^{2} \cdot - 1$ .

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$1 x^{2} + 2 x \cdot - 1 + 3 \cdot - 1 = 0 \cdot - 1$

Multiply $x^{2}$ by $1$ .

$x^{2} + 2 x \cdot - 1 + 3 \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $2$ .

$x^{2} - 2 x + 3 \cdot - 1 = 0 \cdot - 1$

Multiply $3$ by $- 1$ .

$x^{2} - 2 x - 3 = 0 \cdot - 1$

Multiply $0$ by $- 1$ .

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

Factor $x^{2} - 2 x - 3$ using the AC method.

Tap for more steps…

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

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

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 3 = 0$

$x + 1 = 0$

Set the first factor equal to $0$ and solve.

Tap for more steps…

Set the first factor equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set the next factor equal to $0$ and solve.

Tap for more steps…

Set the next factor equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 3) (x + 1) = 0$ true.

$x = 3, - 1$

Exclude the solutions that do not make $\sqrt{2 x + 3} = x$ true.

$x = 3$

Solve for x square root of 2x+3=x

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store