Solve Using the Quadratic Formula x^2-0.2=-0.06x

Problem

x2−0.2=−0.06*x

Solution

1. Rewrite the equation in standard form a*x2+b*x+c=0 by adding 0.06*x to both sides.

x2+0.06*x−0.2=0

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

a=1

b=0.06

c=−0.2

3. Substitute these values into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−0.06±√(,(0.06)2−4*(1)*(−0.2)))/(2*(1))

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

x=(−0.06±√(,0.0036+0.8))/2

x=(−0.06±√(,0.8036))/2

5. Calculate the square root of 0.8036

√(,0.8036)≈0.896437

6. Solve for the two possible values of x

(x_1)=(−0.06+0.896437)/2

(x_1)=0.4182185

(x_2)=(−0.06−0.896437)/2

(x_2)=−0.4782185

Final Answer

x≈0.4182,−0.4782

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