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# Sample math questions: Solve each equation and check for extraneous solution

Solve each equation and check for extraneous solution.

# 41. -----------------
/ 2x^2 - 1 = x

# 42. ------------------------
/ 2x^2 - 3x - 10 = x

Solve the equation

# 85 -----------------------
/ x^2 + 5x = 6

# 91 -----------------------
/ x^2 - 3x = x

Page 533

Find the perfect square trinomial whose first two terms are given.

# 28. w^2 - 5w

# 31 2
X^2 + --- x
3

# 52. 2m^2 - m - 15 = 0

# 58. 2x^2 + 5x -1 = 0

Page 541

Solve each equation by using the quadratic formula.

# 19 v^2 + 8v + 6 = 0

# 21. - x^2 - 5x + 1 = 0

# 23. 2t^2 - 6t + 1 = 0

Page 364
Solve each equation. Watch for extraneous solutions.

# 28. 4 3 x 1
--- + --- = --- -- ----
x x-3 x-3 3

#### Solution Preview

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Need help with solution

Solve each equation and check for extraneous solution.

# 41. -----------------
/ 2x^2 - 1 = x
Solution:
Subtract x on both sides.
2x2 - x- 1 =0.
Write -x as -2x+x.
2x2-2x +x-1 = 0.
Factor out 2x from the first two terms and 1 from the next two.
2x(x-1)+1(x-1) = 0.
Factor out (x-1).
(x-1)(2x+1) = 0.
 (x-1) = 0 or (2x+1) = 0.
x = 1 or x = - ½
Check for extraneous solutions.
Plug in x = 1 in the original equation.
2(1)2 - 1= 1
2 - 1= 1  1 = 1, which is true.
Plug in x= - ½ in the original equation.
2(- ½)2 -1 = (- ½ )
2( ¼ ) - 1 = (- ½ )
½ -1 = (- ½ )
-½ = - ½, which is also true.
Both the solutions satisfy the original equation.
None of the solutions are extraneous.

# 42. ------------------------
/ 2x^2 - 3x - 10 = x
Solution:
2x2-3x-10 = x
1Subtract x on both sides.
2x1-4x-10 =0.
Use quadratic formula to solve for x.
x =
Here a =2 , b= -4 and c = -10.
Plug in the values in the formula.
x =
=
=
=
= 1 
Therefore 1 + and ...

#### Solution Summary

The equations for extraneous solutions are provided.

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