Question

Solve for x:
X2+5x-(a2+a-6)=0.​

Answer 1

Answer:

Let's solve for a.

x2+5x−(2a+a−6)=0

Step 1: Add -x^2 to both sides.

x2−3a+5x+6+−x2=0+−x2

−3a+5x+6=−x2

Step 2: Add -5x to both sides.

−3a+5x+6+−5x=−x2+−5x

−3a+6=−x2−5x

Step 3: Add -6 to both sides.

−3a+6+−6=−x2−5x+−6

−3a=−x2−5x−6

Step 4: Divide both sides by -3.

−3a

−3

=

−x2−5x−6

−3

a=

1

3

x2+

5

3

x+2

Answer:

a=

1

3

x2+

5

3

x+2

Answer 2

${x}^{2} + 5x - ( {a}^{2} + a - 6) = 0 \\ {x}^{2} + 5x - ( {a}^{2} + 3a - 2a - 6) = 0 \\ {x}^{2} + 5x -( a (a + 3) - 2(a + 3)) = 0 \\ {x}^{2} + 5x - (a + 3)(a - 2) = 0 \\ {x}^{2} + (a + 3)x - (a - 2)x - (a + 3)(a - 2) = 0 \\ x(x + a + 3) - (a - 2)(x + a + 3) = 0 \\ (x - a + 2)(x + a + 3) = 0 \\ (x - a + 2) = 0 \: \: \: or \: \: \: (x + a + 3) = 0 \\ x = a - 2 \: \: \: or \: \: \: x = - a - 3$