Find All Complex Solutions square root of 2y+3+4=2

$\sqrt{2 y + 3} + 4 = 2$

Step 1

Move all terms not containing $\sqrt{2 y + 3}$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$\sqrt{2 y + 3} = 2 - 4$

Subtract $4$ from $2$ .

$\sqrt{2 y + 3} = - 2$

Step 2

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

${\sqrt{2 y + 3}}^{2} = {(- 2)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 y + 3}$ as ${(2 y + 3)}^{\frac{1}{2}}$ .

${({(2 y + 3)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Simplify the left side.

Simplify ${({(2 y + 3)}^{\frac{1}{2}})}^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(2 y + 3)}^{1} = {(- 2)}^{2}$

Simplify.

$2 y + 3 = {(- 2)}^{2}$

Simplify the right side.

Raise $- 2$ to the power of $2$ .

$2 y + 3 = 4$

Step 4

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$2 y = 4 - 3$

Subtract $3$ from $4$ .

$2 y = 1$

Divide each term in $2 y = 1$ by $2$ and simplify.

Divide each term in $2 y = 1$ by $2$ .

$\frac{2 y}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{1}{2}$

Divide $y$ by $1$ .

$y = \frac{1}{2}$

Step 5

Exclude the solutions that do not make $\sqrt{2 y + 3} + 4 = 2$ true.

$No solution$

Find All Complex Solutions square root of 2y+3+4=2

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