Final answer:
To write the equations in standard form, rearrange the terms so the equation is set equal to zero. Use the quadratic formula to find the values of x. The two given equations are 3x=x²-5 and -10=2x²-9x.
Step-by-step explanation:
To write an equation in standard form ax²+c=0, we need to rearrange the terms so that the equation is equal to zero. Let's take the given equations one by one:
1. 3x=x²-5
To put it in standard form, subtract 3x from both sides:
x²-3x-5=0
Now we have the equation in standard form. To find the value of x, we can use the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
Plugging in the values a=1, b=-3, and c=-5, we get:
x = (-(-3) ± √((-3)²-4(1)(-5))) / (2(1))
Simplifying further, we have:
x = (3 ± √(9+20)) / 2
x = (3 ± √29) / 2
So, the two possible values of x are (3+√29)/2 and (3-√29)/2.
2. -10=2x²-9x
To write it in standard form, we need to subtract -10 from both sides:
2x²-9x+10=0
This equation is already in standard form. To find the value of x, we can use the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
Plugging in the values a=2, b=-9, and c=10, we get:
x = (-(-9) ± √((-9)²-4(2)(10))) / (2(2))
Simplifying further, we have:
x = (9 ± √(81-80)) / 4
x = (9 ± √1) / 4
So, the two possible values of x are (9+1)/4 and (9-1)/4.