Question

4. Solve the equation using the quadratic formula.

Answer 1

Answer:

A. x = -2, x = 1.25

Step-by-step 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

Answer:

A. x = -2, x = 1.25

Step-by-step 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 = $\frac{-3+\sqrt{9-4x4(-10)} }{2x4}$

Multiply the numbers

x = $\frac{-3+\sqrt{9+160} }{2x4}$

Add the numbers

x = $\frac{-3+\sqrt{169} }{2x4}$

Evaluate the square root

x = $\frac{-3+13}{2x4}$

Multiply the numbers

x = $\frac{-3+13}{8}$

Separate the equations

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

x = $\frac{-3+13}{8}$

x = $\frac{-3-13}{8}$

Solve

Rearrange and isolate the variable to find each solution

x = - 2

x = 1.25