The solution of the equation [tex]\sqrt {x + 10} - 9 = - 7[/tex] is [tex]\boxed{{\mathbf{ - 6}}}[/tex].
Further explanation:
The square root of a number [tex]x[/tex] is a number [tex]y[/tex] if it follows the condition [tex]{y^2} = x[/tex].
The symbol of the square root is [tex]\sqrt {}[/tex].
Given:
The given equation is [tex]\sqrt {x + 10} - 9 = - 7[/tex].
Step by step explanation:
Step 1:
Add 9 both sides of the equation .
[tex]\begin{aligned}\sqrt {x + 10} - 9 + 9 &= - 7 + 9 \hfill \\\sqrt {x + 10}&= 2 \hfill \\\end{aligned}[/tex]
Step 2:
Now square both sides of the equation.
[tex]{\left( {\sqrt {x + 10} } \right)^2} = 4[/tex]
Step 3:
The expression [tex]{\left( {\sqrt x } \right)^2}[/tex] can be written as [tex]x[/tex].
Therefore, the expression [tex]{\left( {\sqrt {x + 10} } \right)^2}[/tex] can be written as [tex]x + 10[/tex].
Step 4:
Now solve the expression [tex]{\left( {\sqrt {x + 10} } \right)^2} = 4[/tex] as,
[tex]\begin{aligned}{\left( {\sqrt {x + 10} } \right)^2} &= 4 \hfill \\x + 10 &= 4 \hfill \\\end{aligned}[/tex]
Step 5:
Now collect the like terms and solve as,
[tex]\begin{aligned}x &= 4 - 10 \hfill\\x &= - 6 \hfill\\\end{aligned}[/tex]
Therefore, the solution of the equation [tex]\sqrt {x + 10} - 9 = - 7[/tex] is [tex]- 6[/tex].
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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
