Solve x^2+(3+2*8/7)x+4+8/7=0

$$x ^ { 2 } + ( 3 + 2 \times \frac { 8 } { 7 } ) x + 4 + \frac { 8 } { 7 } = 0$$

Solve for x

$$x = -\frac{9}{7} = -1\frac{2}{7} \approx -1.285714286$$

$$x=-4$$

Steps Using the Quadratic Formula

Multiply 2 and \frac{8}{7} to get \frac{16}{7}.

$$x^{2}+\left(3+\frac{16}{7}\right)x+4+\frac{8}{7}=0$$

Add 3 and \frac{16}{7} to get \frac{37}{7}.

$$x^{2}+\frac{37}{7}x+4+\frac{8}{7}=0$$

Add 4 and \frac{8}{7} to get \frac{36}{7}.

$$x^{2}+\frac{37}{7}x+\frac{36}{7}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{37}{7} for b, and \frac{36}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{37}{7}±\sqrt{\left(\frac{37}{7}\right)^{2}-4\times \frac{36}{7}}}{2}$$

Square \frac{37}{7} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{37}{7}±\sqrt{\frac{1369}{49}-4\times \frac{36}{7}}}{2}$$

Multiply -4 times \frac{36}{7}.

$$x=\frac{-\frac{37}{7}±\sqrt{\frac{1369}{49}-\frac{144}{7}}}{2}$$

Add \frac{1369}{49} to -\frac{144}{7} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{37}{7}±\sqrt{\frac{361}{49}}}{2}$$

Take the square root of \frac{361}{49}.

$$x=\frac{-\frac{37}{7}±\frac{19}{7}}{2}$$

Now solve the equation x=\frac{-\frac{37}{7}±\frac{19}{7}}{2} when ± is plus. Add -\frac{37}{7} to \frac{19}{7} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{18}{7}}{2}$$

Divide -\frac{18}{7} by 2.

$$x=-\frac{9}{7}$$

Now solve the equation x=\frac{-\frac{37}{7}±\frac{19}{7}}{2} when ± is minus. Subtract \frac{19}{7} from -\frac{37}{7} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=-\frac{9}{7} x=-4$$

Steps for Completing the Square

Multiply 2 and \frac{8}{7} to get \frac{16}{7}.

$$x^{2}+\left(3+\frac{16}{7}\right)x+4+\frac{8}{7}=0$$

Add 3 and \frac{16}{7} to get \frac{37}{7}.

$$x^{2}+\frac{37}{7}x+4+\frac{8}{7}=0$$

Add 4 and \frac{8}{7} to get \frac{36}{7}.

$$x^{2}+\frac{37}{7}x+\frac{36}{7}=0$$

Subtract \frac{36}{7} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+\frac{37}{7}x=-\frac{36}{7}$$

Divide \frac{37}{7}, the coefficient of the x term, by 2 to get \frac{37}{14}. Then add the square of \frac{37}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{37}{7}x+\left(\frac{37}{14}\right)^{2}=-\frac{36}{7}+\left(\frac{37}{14}\right)^{2}$$

Square \frac{37}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{37}{7}x+\frac{1369}{196}=-\frac{36}{7}+\frac{1369}{196}$$

Add -\frac{36}{7} to \frac{1369}{196} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{37}{7}x+\frac{1369}{196}=\frac{361}{196}$$

Factor x^{2}+\frac{37}{7}x+\frac{1369}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{37}{14}\right)^{2}=\frac{361}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{37}{14}\right)^{2}}=\sqrt{\frac{361}{196}}$$

Simplify.

$$x+\frac{37}{14}=\frac{19}{14} x+\frac{37}{14}=-\frac{19}{14}$$

Subtract \frac{37}{14} from both sides of the equation.

$$x=-\frac{9}{7} x=-4$$