Solve the following equation for z. {:[sqrt(4z+9)=z+1],[z=]:}

Question

Solve the following equation for  z.  {:[sqrt(4z+9)=z+1],[z=]:}

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Isolate square root: Isolate the square root on one side of the equation. We have the equation sqrt(4z+9) = z + 1. The square root is already isolated on the left side of the equation.Square both sides: Square both sides of the equation to eliminate the square root. (sqrt(4z+9))^2 = (z + 1)^2 This gives us 4z + 9 = (z + 1)(z + 1).Expand right side: Expand the right side of the equation. 4z + 9 = z^2 + 2z + 1Move terms to one side: Move all terms to one side to set the equation to zero and form a quadratic equation. 0 = z^2 + 2z + 1 - 4z - 9Combine like terms: Combine like terms. 0 = z^2 - 2z - 8Factor quadratic equation: Factor the quadratic equation, if possible. We look for two numbers that multiply to -8 and add to -2. These numbers are -4 and +2. 0 = (z - 4)(z + 2)Solve for z: Solve for z by setting each factor equal to zero. z - 4 = 0 or z + 2 = 0 This gives us z = 4 or z = -2.Check solutions: Check both solutions in the original equation to ensure they do not result in taking the square root of a negative number. For z = 4: sqrt(4(4)+9) = 4 + 1 sqrt(16+9) = 5 sqrt(25) = 5 5 = 5, which is true.  For z = -2: sqrt(4(-2)+9) = -2 + 1 sqrt(-8+9) = -1 sqrt(1) = -1 1 ≠ -1, which is false.  So, z = -2 is not a valid solution because it does not satisfy the original equation.

Solve the following equation for $z$ . $\newline$ $\begin{array}{l} \quad \sqrt{4 z+9}=z+1 \\ z=\square \end{array}$

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Solve the following equation for z z z.\newline4z+9=z+1z=□ \begin{array}{l} \quad \sqrt{4 z+9}=z+1 \\ z=\square \end{array} 4z+9​=z+1z=□​

Solve the following equation for $z$ . $\newline$ $\begin{array}{l} \quad \sqrt{4 z+9}=z+1 \\ z=\square \end{array}$