The solution of the equation \(\sqrt {x + 10} - 9 = - 7\) is \(\boxed{{\mathbf{ - 6}}}\).
Further explanation:
The square root of a number \(x\) is a number \(y\) if it follows the condition \({y^2} = x\).
The symbol of the square root is \(\sqrt {}\).
Given:
The given equation is \(\sqrt {x + 10} - 9 = - 7\).
Step by step explanation:
Step 1:
Add 9 both sides of the equation .
\(\begin{aligned}\sqrt {x + 10} - 9 + 9 &= - 7 + 9 \hfill \\\sqrt {x + 10}&= 2 \hfill \\\end{aligned}\)
Step 2:
Now square both sides of the equation.
\({\left( {\sqrt {x + 10} } \right)^2} = 4\)
Step 3:
The expression \({\left( {\sqrt x } \right)^2}\) can be written as \(x\).
Therefore, the expression \({\left( {\sqrt {x + 10} } \right)^2}\) can be written as \(x + 10\).
Step 4:
Now solve the expression \({\left( {\sqrt {x + 10} } \right)^2} = 4\) as,
\(\begin{aligned}{\left( {\sqrt {x + 10} } \right)^2} &= 4 \hfill \\x + 10 &= 4 \hfill \\\end{aligned}\)
Step 5:
Now collect the like terms and solve as,
\(\begin{aligned}x &= 4 - 10 \hfill\\x &= - 6 \hfill\\\end{aligned}\)
Therefore, the solution of the equation \(\sqrt {x + 10} - 9 = - 7\) is \(- 6\).
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: square, square root, number, add, divide, subtract, expression, symbol, real number, collect, keep aside, linear equation
