Next step, multiply both sides by (.01-x)
.012(.01-x)=.01x+x^2
is the binomial x^2 + .002x-1.2x10^-4
what is the next step
is the answer -.021 and -.023 for x
No. Just solve the quadratic using the quadratic formula.
To solve the equation x^2 + 0.002x - 1.2x10^-4 = 0, you need to use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 0.002, and c = -1.2x10^-4.
Substituting these values into the formula, you get:
x = (-(0.002) ± √((0.002)^2 - 4(1)(-1.2x10^-4))) / (2(1))
Simplifying further, you get:
x = (-0.002 ± √(0.000004 + 4.8x10^-4)) / 2
Combining like terms, you get:
x = (-0.002 ± √(0.0000088)) / 2
x = (-0.002 ± 0.002966) / 2
Now you can calculate two potential solutions:
x1 = (-0.002 + 0.002966) / 2 = 0.000483
x2 = (-0.002 - 0.002966) / 2 = -0.002966
Therefore, the solutions for x are approximately 0.000483 and -0.002966.
To solve the given equation x^2 + 0.002x - 1.2x10^-4 = 0, you can follow these steps:
1. Start with the equation: x^2 + 0.002x - 1.2x10^-4 = 0.
2. Identify the quadratic expression in the equation: x^2 + 0.002x - 1.2x10^-4.
3. Verify if the quadratic expression can be factored. In this case, it cannot be factored easily.
4. Apply the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac))/(2a).
In this case:
a = 1, b = 0.002, and c = -1.2x10^-4.
Plugging in these values, the quadratic formula becomes:
x = (-(0.002) ± √((0.002)^2 - 4(1)(-1.2x10^-4)))/(2(1)).
5. Simplify the expression inside the square root: (0.002)^2 - 4(-1.2x10^-4).
- (0.002)^2 = 4x10^-6.
- 4(-1.2x10^-4) = 4.8x10^-4.
Subtracting these two values: 4x10^-6 - 4.8x10^-4 = -4.7996x10^-4.
6. Substitute the simplified value back into the quadratic formula: x = (-(0.002) ± √(-4.7996x10^-4))/(2(1)).
7. Continue simplifying the expression inside the square root: √(-4.7996x10^-4) = √(-1) * √(4.7996x10^-4).
- √(-1) = i (to represent the imaginary unit).
- √(4.7996x10^-4) = √(4.7996) * √(10^-4) = 0.06924.
So, √(-4.7996x10^-4) = i * 0.06924 = 0.06924i.
8. Substitute the simplified value back into the quadratic formula: x = (-(0.002) ± 0.06924i)/(2(1)).
9. Further simplify the equation: x = (-0.002 ± 0.06924i)/2.
10. Calculate both solutions by dividing:
Solution 1: (-0.002 + 0.06924i)/2 ≈ -0.001 + 0.03462i ≈ -0.001 + 0.0346i.
Solution 2: (-0.002 - 0.06924i)/2 ≈ -0.001 - 0.03462i ≈ -0.001 - 0.0346i.
Therefore, the solutions for x are approximately -0.001 + 0.0346i and -0.001 - 0.0346i.