Question

How do you do the last question using the quadratic formula?

Answer 1

Answer:

$x = -1$

Step-by-step explanation:

To do the last question using the quadratic formula, you first need the equation in standard form.

ax² + bx + c = 0.

To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.

2(x - 2)(x + 1) = x² - 4x - 5        Expand brackets first using FOIL

2(x² + x - 2x - 2) = x² - 4x - 5        Collect like terms in brackets (x - 2x = -x)

2(x² - x - 2) = x² - 4x - 5        Distribute, multiply bracket numbers by "2"

2x² - 2x - 4 = x² - 4x - 5        Now make the equation equal 0

2x² - 2x - 4 - x² = x² - 4x - 5 - x²        Subtract x² from both sides

x² - 2x - 4 = -4x - 5        "x²" eliminated from the right side. Simplify left side.

x² - 2x - 4 + 4x = -4x - 5 + 4x        Add 4x to both sides.

x² + 2x - 4 = -5        "4x" eliminated from right side. Simplify left side.

x² + 2x - 4 + 5 = -5 + 5        Add 5 to both sides to eliminate it on the right.

x² + 2x + 1 = 0               Simplified left side.

This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.

a = 1; b = 2; c = 1

Substitute into the quadratic formula

$x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}$      (Please ignore the Â, it's a formatting error)

$x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}$   Simplify the square root

$x = \frac{-2±\sqrt{0} }{2}$     The square root of 0 is 0.

$x = \frac{-2}{2}$      The numerator can only be -2. Simplify the fraction

$x = -1$         Only one answer for "x".

Whenever the square root equals "0", there will only be one answer for "x".