Solve Using the Quadratic Formula (x+7)(2x+1)=7

Problem

(x+7)*(2*x+1)=7

Solution

1. Expand the left side of the equation using the FOIL method.

2*x2+x+14*x+7=7

2. Simplify the expression by combining like terms.

2*x2+15*x+7=7

3. Subtract 7 from both sides to set the equation to zero in standard form a*x2+b*x+c=0

2*x2+15*x=0

4. Identify the coefficients for the quadratic formula where a=2 b=15 and c=0

x=(−b±√(,b2−4*a*c))/(2*a)

5. Substitute the values into the quadratic formula.

x=(−15±√(,15−4*(2)*(0)))/(2*(2))

6. Simplify the radicand and the denominator.

x=(−15±√(,225))/4

7. Evaluate the square root.

x=(−15±15)/4

8. Solve for both possible values of x

x=(−15+15)/4=0

x=(−15−15)/4=−30/4=−7.5

Final Answer

(x+7)*(2*x+1)=7⇒x=0,x=−7.5

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