How to solve a quadratic equation?

Question

x²+ 30x + 144 = 0

Answer 1

The quadratic formula is derived using the technique of completing the square. When the leading coefficient is 1, often trial and error (or split-the-middle) is the easiest choice When the leading coefficient is 1 and the coefficient of x is an even integer, sometimes going through the process of completing the square gets to the answers fairly quickly.

x² + 30x + 144 = 0

x² + 30x +?? = -144 + ?? (those question marks to be filled in with a value that completes the square)

x² + 30x + 225 = -144 + 225 (the 225 was determined by taking 1/2 of 30 and squaring the result:15² = 225

(x + 15)² = 81 (rewrite the perfect square trinomial as a binomial squared)

x + 15 = ±9 (using the square root property--square root of both sides--note the 81 has two square roots)

x = -15 ± 9

x₁ = -6, x₂ = -24

Those values are also the x-coordinates of the x-intercepts for the parabola:

y = x² + 30x + 144

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Answer 2

There are several ways of finding a solution to an equation

In this case, I think the easiest way is looking at the constant of 144 and writing down the factors of 144 and then whichever two factors went out together equal 30 then that’s a great start to your answer, so

1 times 144

2 times 72

3 times 48

4 times 36

6 times 24

The pair of six and 24 when added together equal 30 so we’re gonna focus on factoring this with six and 30 and then solving for X we are going to get two answers and then we’re going to re-substitute them in to the original equation to see if they make the equation true

(x+6)(x+24)=0

x+6=0 so x=-6

x+24=0 so x=-24

these are solutions -6 and -24

To verify substitute each one individually into the original equation, and you will see that they satisfy the equation to make it equal zero

(-6)^2 + 30(-6) + 144 =0

(-24)^2 + 30(-24) + 144 =0

Answer 3

x² _{+ 30x + 144= 0}

_{You want to solve this equation by using the quadratic formula.}

x = -b +/- √b² -4ac

________________

2a

Step 1 - You want to identify the coefficients

a= 1, b = 30, c= 144

Step 2 - Plug in coefficients

x = -30 +/- √30² - 4 * 1 * 144

_______________________

2*1

Step 3 - break down part 1 (multiply; 4*1) and (multiply 2*1)

x = -30 +/- √30² - 4*144

___________________

2

Step 4 - break down part 2 ( simplify 30² 30*30)

x= -30 +/- √900-4*144

____________________

2

Step 5 - break down part 3 (simplify 4*144)

x= -30 +/- √900 -576

________________

2

Step 6 - break down part 4 (subtract 900-576)

x = -30 +/- √324

___________

2

Step 7 - break down part 5 (find the square root of 324)

x = -30 +/- 18

__________

2

Step 8 - break down part 6 (and and subtract the equation in simplest form)

x = -30 + 18 x= -30 - 18

___________ _____________

2 2

Step 9 - break down part 7 ( simplify each equation in simplest form)

x = -12

___ = -6 x = -48

_____ = -24

2 2

Therefore, _{x1 = -6 x2 = -24}

I hope this helps!

Answer 4

The easiest way is to find out if two numbers will multiply to be 144 AND add to be 30.

These numbers would be 6 and 24. You can find these numbers by starting with

1 and 144

2 and 72

3 and 48

4 and 36

6 and 24. BINGO. These add to be 30 (the coefficient of the middle term)

So your factors are (x + 6) and (x + 24)

Set each one equal to 0 and solve.

x + 6 = 0. and x + 24 = 0

x = -6 and x = -24

Answer 5

Try FOIL.

Here's a hint

x² + 30x + (6)(24)