SOLVE FOR X:
Answers
Solution!!
→ x - 2√x - 8 = 0
Move the expression to the right-hand side and change its sign
→ -2√x = 8 - x
Square both sides of the equation
→ (-2√x)² = (8 - x)²
→ (-2)²(√x)² = (8)² + (x)² - 2(8)(x)
→ 4x = 64 + x² - 16x
Move the expression to the left-hand side and
change its sign
→ - x² + 4x + 16x - 64 = 0
Factor out -x and 16 from the expression
→ - x(x - 4) + 16(x - 4) = 0
Factor out -x + 16 from the expression
→ (- x + 16)(x - 4) = 0
Now atleast one of the factors is zero.
→ - x + 16 = 0
→ x - 4 = 0
→ x = 16
→ x = 4
Now, let's check if the value is the solution of the equation.
→ 16 - 2√16 - 8 = 0
→ 4 - 2√4 - 8 = 0
→ 16 - 2(4) - 8 = 0
→ 4 - 2(2) - 8 = 0
→ 16 - 8 - 8 = 0
→ 4 - 4 - 8 = 0
→ 16 - 16 = 0
→ 4 - 12 = 0
→ 0 = 0
→ -8 ≠ 0
Hence, the value of x is 16.
Topic:
Solving radical equations
Step-by-step explanation:
STEP 1 : Isolate the square root on the left hand side
Original equation
Isolate
Tidy up
STEP 2 : Eliminate the radical on the left hand side
Raise both sides to the second power
After squaring
STEP 3 : Solve the quadratic equation
Rearranged equation
This equation has two rational roots:
STEP 4 : Check that the first solution is correct
Original equation, root isolated, after tidy up
Plug in 16 for x
Simplify
Solution checks !!
Solution is:
STEP 5 : Check that the second solution is correct
Original equation, root isolated, after tidy up
Plug in 4 for x
Simplify
Solution does not check