Solve 2*7x^2+2.2x-1=0

$$2 \cdot 7 x ^ { 2 } + 2.2 x - 1 = 0$$

Solve for x

$$x=-\frac{5}{14}\approx -0.357142857$$

$$x=0.2$$

Steps Using the Quadratic Formula

Multiply 2 and 7 to get 14.

$$14x^{2}+2.2x-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 14 for a, 2.2 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2.2±\sqrt{2.2^{2}-4\times 14\left(-1\right)}}{2\times 14}$$

Square 2.2 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-2.2±\sqrt{4.84-4\times 14\left(-1\right)}}{2\times 14}$$

Multiply -4 times 14.

$$x=\frac{-2.2±\sqrt{4.84-56\left(-1\right)}}{2\times 14}$$

Multiply -56 times -1.

$$x=\frac{-2.2±\sqrt{4.84+56}}{2\times 14}$$

Add 4.84 to 56.

$$x=\frac{-2.2±\sqrt{60.84}}{2\times 14}$$

Take the square root of 60.84.

$$x=\frac{-2.2±\frac{39}{5}}{2\times 14}$$

Multiply 2 times 14.

$$x=\frac{-2.2±\frac{39}{5}}{28}$$

Now solve the equation x=\frac{-2.2±\frac{39}{5}}{28} when ± is plus. Add -2.2 to \frac{39}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{28}{5}}{28}$$

Divide \frac{28}{5} by 28.

$$x=\frac{1}{5}$$

Now solve the equation x=\frac{-2.2±\frac{39}{5}}{28} when ± is minus. Subtract \frac{39}{5} from -2.2 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{10}{28}$$

Reduce the fraction \frac{-10}{28} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{14}$$

The equation is now solved.

$$x=\frac{1}{5} x=-\frac{5}{14}$$

Steps for Completing the Square

Multiply 2 and 7 to get 14.

$$14x^{2}+2.2x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$14x^{2}+2.2x=1$$

Divide both sides by 14.

$$\frac{14x^{2}+2.2x}{14}=\frac{1}{14}$$

Dividing by 14 undoes the multiplication by 14.

$$x^{2}+\frac{2.2}{14}x=\frac{1}{14}$$

Divide 2.2 by 14.

$$x^{2}+\frac{11}{70}x=\frac{1}{14}$$

Divide \frac{11}{70}, the coefficient of the x term, by 2 to get \frac{11}{140}. Then add the square of \frac{11}{140} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{11}{70}x+\frac{11}{140}^{2}=\frac{1}{14}+\frac{11}{140}^{2}$$

Square \frac{11}{140} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{11}{70}x+\frac{121}{19600}=\frac{1}{14}+\frac{121}{19600}$$

Add \frac{1}{14} to \frac{121}{19600} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{11}{70}x+\frac{121}{19600}=\frac{1521}{19600}$$

Factor x^{2}+\frac{11}{70}x+\frac{121}{19600}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{140}\right)^{2}=\frac{1521}{19600}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{140}\right)^{2}}=\sqrt{\frac{1521}{19600}}$$

Simplify.

$$x+\frac{11}{140}=\frac{39}{140} x+\frac{11}{140}=-\frac{39}{140}$$

Subtract \frac{11}{140} from both sides of the equation.

$$x=\frac{1}{5} x=-\frac{5}{14}$$