I assume you can apply the quadratic formula.
3x^2 + 20x - 7
The factors must be of the form
(3x?1)(x?7)
or
(3x?7)(x?1)
where the proper + or - sign must be used to get the +20x. Hint: 3*7 = 21
To solve by completing the square, proceed as in the examples in your text to get a completed square:
3x^2 + 20x = 7
3(x^2 + 20/3 x) = 7
Now add (10/3)^2 inside the parentheses to complete the square:
3(x^2 + 20/3 x + 100/9) = 7 + 3*100/9
3(x + 10/3)^2 = 121/3
(x + 10/3)^2 = 121/9 = (11/3)^2
x + 10/3 = ±11/3
x = 10/3 ± 11/3
x = 7 or -1/3
1a) Solve the each of these equations by factorising the left hand side into a product of linear factors:
(i) x^2 - 6x - 40 = 0
(ii) 3x^2 + 20x - 7 = 0
(b) For each question in part (a), check your solutions by substituting them back into the equation.
3. Solve each equation from Question 1, in the form given below,by completing the square on the left-hand side:
(a) x^2 - 6x = 40
(b) 3x^2 + 20x = 7
4. Solve the equations from Question 1 using the quadratic formula:
x = -b +- √b^2-4ac
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2a
1 answer
1 answer