Solve for x: 4xx−3=2+12x−3 .(1 point)
Responses
no solutions
no solutions
2
2
72
Start Fraction 7 over 2 End Fraction
92
To solve for x, we need to simplify the equation and isolate x on one side.
4x(x-3) = 2 + 12x -3
4x^2 - 12x = -1 + 12x
Rearranging the terms:
4x^2 - 24x + 1 = 0
Now, we can solve for x by factoring, completing the square, or by using the quadratic formula. However, in this case, the equation does not factor easily and cannot be simplified further.
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 4, b = -24, and c = 1:
x = (-(-24) ± √((-24)^2 - 4(4)(1))) / (2(4))
x = (24 ± √(576 - 16)) / 8
x = (24 ± √560) / 8
x = (24 ± 4√35) / 8
Simplifying further:
x = (3 ± √35) / 2
So, the solutions for x are:
x = (3 + √35) / 2
x = (3 - √35) / 2
Therefore, we have two solutions for x: (3 + √35) / 2 and (3 - √35) / 2
To solve the equation 4x^2 - 3 = 2 + 12x - 3, we can start by simplifying both sides of the equation:
4x^2 - 3 = 2 + 12x - 3
4x^2 - 3 = 12x - 1
Next, we can move all terms to one side of the equation:
4x^2 - 12x + 3 = -1
Now, we can rearrange the equation to form a quadratic equation:
4x^2 - 12x + 4 = 0
Next, we can divide all terms by 4 to simplify the equation:
x^2 - 3x + 1 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -3, and c = 1. Substituting these values into the quadratic formula, we get:
x = (3 ± √((-3)^2 - 4(1)(1))) / (2(1))
x = (3 ± √(9 - 4)) / 2
x = (3 ± √5) / 2
Therefore, the solution to the equation 4x^2 - 3 = 2 + 12x - 3 is:
x = (3 + √5) / 2 and x = (3 - √5) / 2
To solve for x in the equation 4x/(x-3) = 2 + 12/(x-3), we need to eliminate the denominator by multiplying both sides of the equation by (x-3).
So, we have:
4x = (2 + 12/(x-3))(x-3)
Next, distribute the (x-3) term on the right side of the equation:
4x = 2(x-3) + 12
Multiply on both sides to simplify:
4x = 2x - 6 + 12
Combine like terms:
4x = 2x + 6
Subtract 2x from both sides:
2x = 6
Finally, divide both sides by 2:
x = 3
Therefore, the value of x that satisfies the equation is 3.