4x^2/[(1.5-x)(2.0-2x)^2] =

= 2.72 x 10^11

solve for x

I don't think you will get the answer on your calculator.

To solve for x in the equation 4x^2/[(1.5-x)(2.0-2x)^2] = 2.72 x 10^11, we will follow the steps below:

Step 1: Multiply both sides of the equation by [(1.5-x)(2.0-2x)^2] to eliminate the denominator:

4x^2 = 2.72 x 10^11 * [(1.5-x)(2.0-2x)^2]

Step 2: Distribute the right side of the equation:

4x^2 = 2.72 x 10^11 * [(3 - 1.5x - 2x)(3 - 1.5x - 2x)^2]

Step 3: Simplify the equation by expanding and combining like terms:

4x^2 = 2.72 x 10^11 * [(3 - 1.5x - 2x)(3 - 1.5x - 2x)^2]
4x^2 = 2.72 x 10^11 * [(3 - 3x - 1.5x + 2.25x^2 + 3x^2 - 4.5x^2)]

4x^2 = 2.72 x 10^11 * [(3 - 4.5x + 0.25x^2)]

4x^2 = 2.72 x 10^11 * (3 - 4.5x + 0.25x^2)

Step 4: Distribute the right side of the equation:

4x^2 = 8.16 x 10^11 - 12.24 x 10^11x + 0.68 x 10^11x^2

4x^2 = 8.16 x 10^11 - 12.24 x 10^11x + 0.68 x 10^11x^2

Step 5: Move all terms to one side of the equation:

0 = 0.68 x 10^11x^2 - 12.24 x 10^11x + 8.16 x 10^11

Step 6: Set the equation equal to zero and divide through by 10^11 to simplify:

0 = 0.68x^2 - 12.24x + 8.16

Step 7: Solve the quadratic equation. You can use the quadratic formula to find the values of x that satisfy the equation:

x = (-b ± √(b^2 - 4ac))/2a

In our case, a = 0.68, b = -12.24, and c = 8.16.

x = (-(-12.24) ± √((-12.24)^2 - 4(0.68)(8.16))) / (2 * 0.68)
x = (12.24 ± √(150 + 22.4896)) / 1.36
x = (12.24 ± √(172.4896)) / 1.36
x = (12.24 ± 13.1203) / 1.36

Therefore, the possible solutions for x are:

x1 ≈ (12.24 + 13.1203) / 1.36
x1 ≈ 25.3603 / 1.36
x1 ≈ 18.6687

x2 ≈ (12.24 - 13.1203) / 1.36
x2 ≈ -0.8803 / 1.36
x2 ≈ -0.6478

Therefore, the solutions for x are approximately x ≈ 18.6687 and x ≈ -0.6478.