Answer:
Step-by-step explanation:
The standard form of a quadratic equation is expressed as
ax² + bx + c = 0
The given quadratic equation is expressed as
7x = 3x² - 1
Rearranging it so that it will be in the standard form, it becomes
3x² - 7x - 1 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 3
b = - 7
c = - 1
Therefore,
x = [- - 7 ± √(- 7² - 4 × 3 × - 1)]/2 × 3
x = [7 ± √(49 - - 12)]/6
x = [7 ± √61]/6
x = (7 + √61)/6 or x = (7 - √61)/6
x = (7 + 7.81)/6 or (7 - 7.81)/6
x = 2.468 or x = - 0.135
Answer:
X = 7.41 OR -0.81
Step-by-step explanation:
If the equation is 7x = 3x² - 1?.
We can rearrange it to give us a quadratic equation.
3x² - 7x - 1 = 0
Sum of roots = -7x
Product of roots = -3x
Obviously, no two numbers will give us -7 and -3 as it's sum and Product.
Let's employ, the formula method.
X = (-b ± √ b² - 4ac ) / 2a
a = 3
b= -7
c= -1
X = -(-7) ± √ -7² - 4*3*-1 / 2*3
X = (7 ± √ 49 + 12) / 6
X = (7 ± √ 61 ) / 6
X = (7 ± 7.81 ) / 2
X = (7+7.81)/2. OR. (7 - 7.81) / 2
X = 14.81 / 2. OR. -0.81 / 2
X = 7.41 OR -0.41
