Question

solve the quadratic equation 3x²-x-7 = 0 give your answer correct to two decimal places​

Answer 1

Answer:

x=1.7032. or. x=-1.3699

Step-by-step explanation:

3x^2-x-7=0

a=3

b=-1

c=-7

x=1+-[√{(-1)^2-(4*3*-7)}]÷2*3

x=1+-[√(1+84)]÷6

x=1+-√85/6

x=1+√85/6. or. x=1-√85/6

x=(1+9.2195)/6. or. x=(1-9.2195)/6

x=1.7032. or. x=-1.3699

Answer 2

${ \boxed { \boxed{ \bold \red{Step \: 1 : }}}}$

Use the quadratic formula

$\bold{x = \frac{ - b \underline + \sqrt{ {b}^{2} } - 4ac}{2a} }$

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

$\bold{3x²-x-7 = 0}$

a=3

b=-1

c=-7

$\bold{x = \frac{- ( - 1) \underline + \sqrt{( - 1) {}^{2} } - 4 \times 3( - 7) }{2 \times 3} }$

${ \boxed { \boxed{ \bold \red{Step \: 2: }}}}$

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Multiply the numbers

$\bold{x = \frac{1 \underline + \sqrt{85} }{6} }$

${ \boxed { \boxed{ \bold \red{Step \: 3: }}}}$

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

$\bold{x = \frac{1 + \sqrt{85} }{6} }$

$\bold{x = \frac{1 - \sqrt{85} }{6} }$

${ \boxed { \boxed{ \bold \red{Step \: 4: }}}}$

Solve

Rearrange and isolate the variable to find each solution

$\bold{x = \frac{1 + \sqrt{85} }{6} }$

$\bold{x = \frac{1 - \sqrt{85} }{6} }$

Solution:

$\bold{x = \frac{1 \underline + \sqrt{85} }{6} }$

$\bold{\therefore \: x = 1.70 \: or \: -1.36 }(approx)$

Therefore, correct upto 2 decimal places the value of x will be either 1.70 or -1.36(approx).