Solve Using the Quadratic Formula x^2+10x-3=0

Problem

x2+10*x−3=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=1

b=10

c=−3

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−10±√(,10−4*(1)*(−3)))/(2*(1))

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

x=(−10±√(,100+12))/2

x=(−10±√(,112))/2

4. Factor the square root by finding the largest perfect square factor of 112

√(,112)=√(,16⋅7)

√(,112)=4√(,7)

5. Substitute the simplified radical back into the equation.

x=(−10±4√(,7))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=−5±2√(,7)

Final Answer

x=−5±2√(,7)

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