Solve Using the Quadratic Formula 4b^2+8b+7=4

Problem

4*b2+8*b+7=4

Solution

1. Set the equation to zero by subtracting 4 from both sides to put the quadratic in standard form a*b2+b*b+c=0

4*b2+8*b+3=0

2. Identify the coefficients a b and c for use in the quadratic formula.

a=4

b=8

c=3

3. Apply the quadratic formula b=(−b±√(,b2−4*a*c))/(2*a) by substituting the identified values.

b=(−8±√(,8−4*(4)*(3)))/(2*(4))

4. Simplify the radicand by calculating the square and the product within the square root.

b=(−8±√(,64−48))/8

b=(−8±√(,16))/8

5. Evaluate the square root and simplify the expression for both possible values.

b=(−8±4)/8

6. Solve for both cases to find the two roots of the equation.

(b_1)=(−8+4)/8=(−4)/8=−1/2

(b_2)=(−8−4)/8=(−12)/8=−3/2

Final Answer

b=−1/2,−3/2

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