Question

PLEASE HELP!! Solve x^2=81 and x^2-18x=7. Please show your work!

Answer 1

Answer:

x² = 81 , x = ± 9

x² - 18x = 7 : x = 9 ± √(22)

Step-by-step explanation:

x² = 81

simply take the square root of both sides

x = ± 9

x² - 18x = 7

This question is a bit more complicated as there is a variable with a power as well as a variable with no power. To solve for x we are going to have to put the equation in quadratic form then solve using the quadratic equation

x² - 18x = 7

put the equation in quadratic form by subtracting 7 from both sides so that the equation is equal to 0

x² - 18x - 7 = 0

we can now solve for x using the quadratic equation

recall the quadratic equation : $x=\frac{-b+\sqrt{b^2-4ac} }{2a}$

where the value of a,b and c are derived from the equation

remember the equation is in quadratic form ax² + bx + c = 0

so ax² + bx + c = 0 : x² - 18x - 7 = 0

knowing this we can assign variables, a = 1 , b = -18 and c = -7

now we plug in the variables into the quadratic equation

recall equation : $x=\frac{-b+\sqrt{b^2-4ac} }{2a}$

a = 1 , b = -18 and c = -7

plug in values

$x=\frac{-(-18)+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}$

remove parenthesis

$x=\frac{18+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}$

simplify exponent

$x=\frac{18+\sqrt{324-4(1)(-7)} }{2(1)}$

simplify multiplication in square root and on denominator

$x=\frac{18+\sqrt{324+28} }{2}$

simplify addition

$x=\frac{18+\sqrt{352} }{2}$

simplify radical

$x=\frac{18+4\sqrt{22} }{2}$

simplify fraction

$x=9+or-\sqrt{22}$

and we are done!