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Question
\sqrt{2x+9}-5=0
Solve the equation
x=8
Evaluate
\sqrt{2x+9}-5=0
Find the domain
More Steps
Evaluate
2x+9\geq 0
Move the constant to the right side
2x\geq 0-9
Removing 0 doesn't change the value,so remove it from the expression
2x\geq -9
Divide both sides
\frac{2x}{2}\geq \frac{-9}{2}
Divide the numbers
x\geq \frac{-9}{2}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x\geq -\frac{9}{2}
\sqrt{2x+9}-5=0,x\geq -\frac{9}{2}
Move the constant to the right-hand side and change its sign
\sqrt{2x+9}=0+5
Removing 0 doesn't change the value,so remove it from the expression
\sqrt{2x+9}=5
\text{Raise both sides of the equation to the }2\text{-th power to eliminate the isolated }2\text{-th root}
\left(\sqrt{2x+9}\right)^{2}=5^{2}
Evaluate the power
2x+9=25
Move the constant to the right-hand side and change its sign
2x=25-9
Subtract the numbers
2x=16
Divide both sides
\frac{2x}{2}=\frac{16}{2}
Divide the numbers
x=\frac{16}{2}
Divide the numbers
More Steps
Evaluate
\frac{16}{2}
Reduce the numbers
\frac{8}{1}
Calculate
8
x=8
Check if the solution is in the defined range
x=8,x\geq -\frac{9}{2}
Find the intersection of the solution and the defined range
x=8
Solution
More Steps
Check the solution
\sqrt{2\times 8+9}-5=0
Simplify
0=0
Evaluate
\textrm{true}
x=8
Show Solutions
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