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4x square+ 8 x - 5=0

4 {x}^(2) + 8x - 5 = 0


User Galzor
by
8.8k points

2 Answers

3 votes

Answer:
((1)/(2) , -(5)/(2) )

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

User BarryPye
by
8.2k points
4 votes

Answer:


x = (1)/(2)


x = -(5)/(2)

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!

User Stefan Vogt
by
8.1k points

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