Question

4x square+ 8 x - 5=0" title="4 {x}^{2} + 8x - 5 = 0" alt="4 {x}^{2} + 8x - 5 = 0" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$x = \frac{1}{2}$

$x = -\frac{5}{2}$

Step-by-step explanation:

Solve Using the Quadratic Formula

     4x^2 + 8x − 5 = 0

Use the quadratic formula to find the solutions.

    −b ± √b^2 − 4 (ac)

     -------------------------

               2a

Substitute the values a = 4, b = 8, and c = −5 into the quadratic formula and solve for x.

    −8 ± √82 − 4 ⋅ (4 ⋅ −5)

     -------------------------

              2 ⋅ 4

Simplify the numerator.

Raise 8 to the p ower of 2.

     −8 ± √64 − 4 ⋅ 4 ⋅ −5

x=     ---------------------------

               2 ⋅ 4

Multiply −4 by 4.

        −8 ± √64 − 16 ⋅ −5

x =       -------------------------

                2 ⋅ 4

Multiply −16 by −5.

        −8 ± √64 + 80

x =       -------------------

               2 ⋅ 4

Add 64 and 80.

        −8 ± √144

x =        --------------

             2 ⋅ 4

Rewrite 144 as 12^2.

        −8 ± √122

x =       ------------

            2 ⋅ 4

Pull terms out from under the radical, assuming positive real numbers.

multiply 2 by 4          

        −8 ± 12

x=     ------------

            8

simplify

    −2 ± 3

x=   ---------

        2

The final answer is the combination of both solutions.

x= 1/2, -5/2

Hope this helped!

Answer 2

Answer: $(\frac{1}{2} , -\frac{5}{2} )$

Step-by-step explanation:

Solve Using the Quadratic Formula

      4x^2 + 8x − 5 = 0

Use the quadratic formula to find the solutions.

     −b ± √b^2 − 4 (ac)

      -------------------------

                2a

Substitute the values a = 4, b = 8, and c = −5 into the quadratic formula and solve for x.

     −8 ± √82 − 4 ⋅ (4 ⋅ −5)

      -------------------------

               2 ⋅ 4

Simplify the numerator.

Raise 8 to the p ower of 2.

      −8 ± √64 − 4 ⋅ 4 ⋅ −5

x=     ---------------------------

                2 ⋅ 4

 Multiply −4 by 4.

         −8 ± √64 − 16 ⋅ −5

x =       -------------------------

                 2 ⋅ 4

Multiply −16 by −5.

         −8 ± √64 + 80

x =       -------------------

                2 ⋅ 4

Add 64 and 80.

         −8 ± √144

x =        --------------

              2 ⋅ 4

Rewrite 144 as 12^2.

         −8 ± √122

x =       ------------

             2 ⋅ 4

Pull terms out from under the radical, assuming positive real numbers.

multiply 2 by 4          

         −8 ± 12

x=     ------------

             8

simplify

     −2 ± 3

x=   ---------

         2

The final answer is the combination of both solutions.

x= 1/2, -5/2