Question

Solve the equation. 7x = 3x^2 - 1

Answer 1

X = 7.41 OR -0.81

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

Answer 2

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