Answer:
1) 1x² - 9x - 109 = 0
2) 3x² -12x -15 = 0
3) 3x² + 13x - 27 = 0
4) 6x² + 84x + 236 = 0
5) -16x² + 8x + 383 = 0
Explanation:
The standard form of the quadratic equation is ax² + bx + c where a, b and c are constants.
So we have to convert each of the equations into a form that resembles the above
(1) 11x² -98 = 11 + 9x
- Simplify both sides of the equation.
11x²−98 = 9x+11
- Subtract 9x+11 from both sides.
11x²−98−(9x+11)=9x+11−(9x+11)
==> 11x² -98 -9x - 11 = 0
==> 11x² - 9x - 109 = 0 (Answer)
with a = 11, b = -9, c = -109
(2) (2x - 1)² = (x + 4) ²
- Simplify both sides of the equation
Using the fact that (a + b)²:
(2x - 1 )² = 4x² -4x + 1 (a = 2x, b = -1)
(x +4 )² = x² + 8x + 16 (a = x, b = 4)
==> 4x² -4x + 1 = x² + 8x + 16
==> 4x² -4x + 1 - (x² + 8x + 16) = 0
==> 4x² -4x + 1 - x² - 8x - 16 = 0
==> 3x² -12x -15 = 0 (Answer)
With a=3, b=-12, c=-15
(3) 4x² + 2x − 9 = (x − 2)(x − 9)
- Simplify (x−2)(x−9)
(x - 2) (X - 9) = x² - 9x - 2x + 18 (use FOIL method)
- 4x² + 2x − 9 = x² - 9x - 2x + 18 = x² - 11x + 18
4x² + 2x - 9 - (x² - 11x + 18) = 0
4x² + 2x - 9 - x² + 11x - 18 = 0
3x² + 13x - 27 = 0 (Answer)
(4) 0 = 6(x +7 )² - 58
- Switch sides:
6(x +7 )² - 58 = 0
- Simplify (x + 7)²
(x + 7)² = x² + 14x + 49
- Simplify 6(x² + 14x + 49) - 58 = 0
6(x² + 14x + 49) - 58 = 0
==> 6x² + 84x + 294 - 58 = 0
==> 6x² + 84x + 236 = 0 (Answer)
with a = 6, b = 84 and c = 236
(5) -1/2 ( x - 1/4 )² + 12 = 0
- Calculate
==>
- -1/2 ( x - 1/4 )² + 12 = 0
==>
- Multiply both sides by 32
==> -16x² + 8x - 1 + 384 = 0
==> -16x² + 8x + 383 = 0 (Answer)
with a = -16, b = 8 and c = 383