Answer:
[tex]x = -1[/tex]
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
[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex] (Please ignore the Â, it's a formatting error)
[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex] Simplify the square root
[tex]x = \frac{-2±\sqrt{0} }{2}[/tex] The square root of 0 is 0.
[tex]x = \frac{-2}{2}[/tex] The numerator can only be -2. Simplify the fraction
[tex]x = -1[/tex] Only one answer for "x".
Whenever the square root equals "0", there will only be one answer for "x".
