Square of sum: Resulting in a quadratic equation

Solve the following equation:

$(x+3)^2+2x^2=18$

$x_1=1,x_2=-3$

Find X

$7=5x^2+8x+(x+4)^2$

$-\frac{4}{3}\pm\frac{\sqrt{10}}{6}$

Find X

$(3x+1)^2+8=12$

$x_1=\frac{1}{3},x_2=-1$

Solve the following equation:

$\frac{1}{(x+1)^2}+\frac{1}{x+1}=1$

$-\frac{1}{2}[1\pm\sqrt{5}\rbrack$

Given the equation. Find its solution

$13x^2+4x=8(x+3)^2$

$x_1=10.21,x_2=-1.41$

Solve the following equation:

$(-x+1)^2=(2x+1)^2$

$x_1=0,x_2=-2$

$\frac{(\frac{1}{x}+\frac{1}{2})^2}{(\frac{1}{x}+\frac{1}{3})^2}=\frac{81}{64}$

Find X

$x=1,-\frac{17}{7}$

Solve the following equation:

$(x+3)^2=2x+5$

$x=-2$

Solve the equation

$2x^2-2x=(x+1)^2$

Answers a + b

Find X

$7x+1+(2x+3)^2=(4x+2)^2$

$\frac{1\pm\sqrt{33}}{8}$

Solve the following equation:

$\frac{x^3+1}{(x+1)^2}=x$

$x=\frac{1}{2}$

Solve the following system of equations:

$\begin{cases} \sqrt{x}+\sqrt{y}=\sqrt{\sqrt{61}+6} \\ xy=9 \end{cases}$

$x=\frac{\sqrt{61}}{2}-2.5$

$y=\frac{\sqrt{61}}{2}+2.5$

or

$x=\frac{\sqrt{61}}{2}+2.5$

$y=\frac{\sqrt{61}}{2}-2.5$

Solve the following equation:

$ax^2+5a+x=(3+a)x^2-(x+a)^2$

$-3.644\ge a,-0.023\le a$