Solve for x x^2+9x-4=x+2

Problem

x2+9*x−4=x+2

Solution

1. Subtract x and 2 from both sides to set the quadratic equation to zero.

x2+9*x−4−x−2=0

x2+8*x−6=0

2. Identify the coefficients for the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) where a=1 b=8 and c=−6

a=1

b=8

c=−6

3. Substitute the values into the quadratic formula.

x=(−8±√(,8−4*(1)*(−6)))/(2*(1))

4. Simplify the expression inside the square root (the discriminant).

x=(−8±√(,64+24))/2

x=(−8±√(,88))/2

5. Simplify the radical by factoring out the largest perfect square.

x=(−8±√(,4⋅22))/2

x=(−8±2√(,22))/2

6. Divide each term in the numerator by the denominator.

x=−4±√(,22)

Final Answer

x=−4±√(,22)

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