# How to solve x^2 - 6x + 9 = 20 using the Square Root Property

Question
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How to solve $$\displaystyle{x}^{{2}}-{6}{x}+{9}={20}$$ using the Square Root Property

2020-11-30
$$\displaystyle{x}^{{2}}-{6}{x}+{9}={20}$$ factor the left side $$\displaystyle{\left({x}-{3}\right)}^{{2}}={20}$$ now take the square root of each side $$\displaystyle{x}-{3}=+{\quad\text{or}\quad}-\sqrt{{{20}}}$$ $$\displaystyle{x}=\sqrt{{{20}}}+{3}{\quad\text{or}\quad}{x}=-\sqrt{{{20}}}-{3}$$ $$\displaystyle{x}={2}\sqrt{{{5}}}+{3}{\quad\text{or}\quad}{x}=-{2}\sqrt{{{5}}}-{3}$$

### Relevant Questions

Consider the following system of llinear equations.
$$\displaystyle\frac{{1}}{{3}}{x}+{y}=\frac{{5}}{{4}}$$
$$\displaystyle\frac{{2}}{{3}}{x}-\frac{{4}}{{3}}{y}=\frac{{5}}{{3}}$$
Part A: $$\displaystyle\frac{{{W}\hat{\propto}{e}{r}{t}{y}}}{{\propto{e}{r}{t}{i}{e}{s}}}$$ can be used to write an equivalent system?
Part B: Write an equivalent system and use elimination method to solve for x and y.
Solve the equivalent equations
$$\displaystyle\frac{{{3}{x}+{2}}}{{5}}={7}$$
and
x + 9 = 20
Which of the following equations have the same solution set? Give reasons for your answers that do not depend on solving the equations.
l.$$x-5=3x+7$$
ll.$$3x-6=7x+8$$
lll.$$15x-9=6x+24$$
lV.$$6x-16=14x+12$$
V.$$9x+21=3x-15$$
Vl.$$-0.05+\frac{x}{100}=3\frac{x}{100}+0.07$$
Solve by completing the square $$\displaystyle{x}^{{2}}-{x}-{7}={0}$$
Solve the following systems of equations by using the addition (elimination) method.
x+2y=2 and -3x-6y=-6
System of equations. Use matrices to solve
2x+y=-10
6x-3y=6
When solving systems of equations we have at least two unknowns. A common example of a system of equations is a price problem. For example, Jacob has 60 coins consisting of quarters and dimes.
The coins combined value is \$9.45. Find out how many of each (quarters and dimes) Jacob has.
1.What do the unknowns in this system represent and what are the two equations that that need to be solved?
2.Finally, solve the system of equations.