Solve for x: √(2x+9) + x = 13
step by step solution required..
Answers
Answer:
The value of x is 8.
Step-by-step-explanation:
We have given that,
√( 2x + 9 ) + x = 13
We have to find the value of x.
√( 2x + 9 ) + x = 13
⇒ √( 2x + 9 ) = 13 - x
⇒ [ √( 2x + 9 ) ]² = ( 13 - x )² - - [ Squaring both sides ]
⇒ 2x + 9 = ( 13 )² - 2 * 13 * x + x² - - [ ( a - b )² = a² - 2ab + b² ]
⇒ 2x + 9 = 169 - 26x + x²
⇒ 169 - 26x + x² = 2x + 9
⇒ x² - 26x + 169 = 2x + 9
⇒ x² - 26x + 169 - 2x - 9 = 0
⇒ x² - 26x - 2x + 169 - 9 = 0
⇒ x² - 28x + 160 = 0
⇒ x² - ( 20 + 8 ) x + 160 = 0
⇒ x² - 20x - 8x + 160 = 0
⇒ x ( x - 20 ) - 8 ( x - 20 ) = 0
⇒ ( x - 20 ) ( x - 8 ) = 0
⇒ x - 20 = 0 or x - 8 = 0
⇒ x = 20 or x = 8
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Verification:
The given equation is √( 2x + 9 ) + x = 13.
We have x = 20 or x = 8.
By substituting x = 20 in the LHS of the given equation, we get,
LHS = √( 2x + 9 ) + x
⇒ LHS = √( 2 * 20 + 9 ) + 20
⇒ LHS = √( 40 + 9 ) + 20
⇒ LHS = √49 + 20
⇒ LHS = 7 + 20
⇒ LHS = 27
RHS = 13
∴ LHS ≠ RHS
∴ x = 20 is not the solution of the given equation.
Now, by substituting x = 8 in the LHS of the given equation, we get,
LHS = √( 2x + 9 ) + x
⇒ LHS = √( 2 * 8 + 9 ) + 8
⇒ LHS = √( 16 + 9 ) + 8
⇒ LHS = √25 + 8
⇒ LHS = 5 + 8
⇒ LHS = 13
RHS = 13
∴ LHS = RHS
∴ x = 8 is the solution of the given equation.