Question

4. Solve the equation using the quadratic formula.

4x^2+3x-10 = 0
A.x= -2, x= 1.25
B.X= -2, x= 2
C.x= -1.25, x= 2
D.x= -1.25, x= 1.25​

Answer 1

A. x = -2, x = 1.25

Explanation:

Use the sum-product pattern

4x² + 3x - 10 = 0

4x² + 8x - 5x - 10 = 0

Common factor from the two pairs

(4x² + 8x) + (-5x - 10) = 0

4x (x + 2) - 5 (x + 2) = 0

Rewrite in factored form

4x (x + 2) - 5 (x + 2) = 0

(4x - 5)(x + 2) = 0

Create separate equations

(4x - 5)(x + 2) = 0

4x - 5 = 0

x + 2 = 0

Solve

Rearrange and isolate the variable to find each solution

x = 1.25

x = - 2

Answer 2

A. x = -2, x = 1.25

Explanation:

Use the quadratic formula

x =
`\frac{-b+\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.

4x² + 3x - 10 = 0

a = 4

b = 3

c = - 10

x =
`\frac{-3+\sqrt{3^(2)-4x4(-10) } }{2x4}`

Simplify

Evaluate the exponent

x =
`(-3+√(9-4x4(-10)) )/(2x4)`

Multiply the numbers

x =
`(-3+√(9+160) )/(2x4)`

Add the numbers

x =
`(-3+√(169) )/(2x4)`

Evaluate the square root

x =
`(-3+13)/(2x4)`

Multiply the numbers

x =
`(-3+13)/(8)`

Separate the equations

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

x =
`(-3+13)/(8)`

x =
`(-3-13)/(8)`

Solve

Rearrange and isolate the variable to find each solution

x = - 2

x = 1.25