I don't understand what to do at all, I've several like this if someone could explain this one i could maybe undersatnd what to do with the rest. Thanks!!
"Factorise, then solve the equation
x^2=5x-36=0
then explain how you could use your answer to solve 5x^2+25x-180=0
What are the solutions?"
I think your equation was meant to be
x^2+5x-36=0
(x+9)(x-4) = 0
x+9=0 or x-4=0
x = -9 or x = 4
for your second equation:
5x^2+25x-180=0
divide each term by 5 to get
x^2+5x-36=0 , the same equation as above.
i think you mean,
x^2 + 5x - 36 = 0
to factor this, first we get the factors of the constant (which is 36),, the factors of 36 are:
+- 1, 2, 3, 4, 6, 9, 12, 18, 36
now, we see from the given equation that 36 is negative,, thus we choose two factors from this set which are in opposite signs (because positive * negative is negative)
and another condition is that the factors must have a sum of +5 (the 5 is found from the second term of the equation)
now we check each pair,, for instance, we choose 3 and -12:
3*(-12) = 36
3 + (-12) = -9
since the sum is not equal to 5, we choose another pair,, let's try -4 and 9:
9*(-4) = 36
9 + (-4) = 5
since the sum is now equal to 5, then we use -4 and 9 as:
(x - 4)(x + 9) = 0
for the second question, we notice that 5 can be factored out from each term,, thus:
5x^2 + 25x - 180 = 0
5(x^2 + 5x - 36) = 0
which is the equation in the first,, thus factoring:
5(x-4)(x+9) = 0
hope this helps~ :)
Please proofread your questions before you post them.
5x^2 + 25x - 180 = 0
Find two factors for each of the end terms (5,1) and (30,6), (5,36), (3,60), (12,15) or (10,18) that will add to give the middle term. Don't ignore the signs.
With your data, I cannot do that. Do you have typos?
To factorize and solve the equation x^2 = 5x - 36 = 0, we need to rearrange it into quadratic form where one side is zero.
Step 1: Rewrite the equation as x^2 - 5x + 36 = 0.
Step 2: Factorize the quadratic equation. In this case, we need to find two numbers whose product is 36 and whose sum is -5. The numbers -4 and -9 satisfy these conditions, so we can factorize the equation as (x - 4)(x - 9) = 0.
Step 3: Set each factor equal to zero to solve for x.
x - 4 = 0
x - 9 = 0
Step 4: Solve for x in each equation.
x = 4
x = 9
Therefore, the solutions to the equation x^2 = 5x - 36 = 0 are x = 4 and x = 9.
Now, let's move on to the second part of the question: "how could you use your answer to solve 5x^2 + 25x - 180 = 0?"
We can use the solutions from the previous equation (x = 4 and x = 9) to solve 5x^2 + 25x - 180 = 0.
Step 1: Substitute the values of x into the equation.
For x = 4: 5(4)^2 + 25(4) - 180 = 0
For x = 9: 5(9)^2 + 25(9) - 180 = 0
Step 2: Simplify and solve the equations.
For x = 4: 80 + 100 - 180 = 0
-180 + 180 = 0
0 = 0
For x = 9: 405 + 225 - 180 = 0
405 + 225 - 180 = 0
450 = 0 (which is not true)
Therefore, the only solution that satisfies the equation 5x^2 + 25x - 180 = 0 is x = 4.