X-3x(1-12x)=11-(5-6x)(6x+5)
To solve the equation x - 3x(1 - 12x) = 11 - (5 - 6x)(6x + 5), we can follow these steps:
Simplify both sides of the equation: x - 3x + 36x^2 = 11 - (30x^2 - 11x + 30x - 25)
Combine like terms: -2x + 36x^2 = 11 - 30x^2 + 1x - 30x + 25
Simplify further: 36x^2 + 2x - 11x + 30x + 30x^2 = 11 + 25 - 30x^2 + 30x
Combine like terms again: 66x^2 - 9x = 36 - 30x^2 + 30x
Rearrange the equation to bring all terms to one side: 66x^2 - 9x - 36 + 30x^2 - 30x = 0
Combine like terms: 96x^2 - 39x - 36 = 0
Now, this is a quadratic equation in the form of ax^2 + bx + c = 0.
To solve this quadratic equation, you can either factor it, complete the square, or use the quadratic formula.
Let's solve it using the quadratic formula:
- Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 96, b = -39, and c = -36.
x = (-(-39) ± √((-39)^2 - 4 * 96 * (-36))) / (2 * 96)
x = (39 ± √(1521 + 13824)) / 192
x = (39 ± √(15345)) / 192
- Simplify the square root: x = (39 ± √(3 * 5115)) / 192
x = (39 ± √(3) * √(5115)) / 192
x = (39 ± √(3) * 71.545) / 192
At this point, we have two possible solutions, one using the positive sign and one using the negative sign.
- Calculate the solutions: x1 = (39 + √(3) * 71.545) / 192 ≈ 0.226 x2 = (39 - √(3) * 71.545) / 192 ≈ -0.332
Therefore, the solutions to the equation x - 3x(1 - 12x) = 11 - (5 - 6x)(6x + 5) are approximately x1 ≈ 0.226 and x2 ≈ -0.332.
