Question

(0.1)^3+2x=(0.1)^2-x^2

Answer 1

$0.1^{3+2x}=(0.1)^{2-x^2} \\ -x^2+2=3+2x \\ x^2+2x+1=0 \\ (x+1)^2=0 \\ x=-1$

Answer 2

To solve the equation (0.1)^3 + 2x = (0.1)^2 - x^2, we can follow these steps:

Step 1: Simplify the equation. Raising 0.1 to a power is the same as multiplying it by itself that many times. (0.1)^3 + 2x = (0.01) - x^2

Step 2: Rearrange the equation. Move all terms to one side of the equation to set it equal to zero. (0.1)^3 + 2x + x^2 - 0.01 = 0

Step 3: Solve the quadratic equation. Rearrange the terms to form a quadratic equation in standard form: ax^2 + bx + c = 0. x^2 + 2x - 0.01 + (0.1)^3 = 0

Step 4: Use the quadratic formula. Apply the quadratic formula to solve for x: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case: a = 1 b = 2 c = -0.01 + (0.1)^3

Plugging in these values into the quadratic formula, we get: x = (-2 ± √(2^2 - 4(1)(-0.01 + (0.1)^3))) / (2(1))

Simplifying further: x = (-2 ± √(4 + 0.04 - 0.4^3)) / 2

x = (-2 ± √(4 + 0.04 - 0.064)) / 2

x = (-2 ± √(4 - 0.004)) / 2

x = (-2 ± √3.996) / 2

x = (-2 ± 1.999) / 2

x = (-2 + 1.999) / 2 or x = (-2 - 1.999) / 2

x = -0.001 / 2 or x = -3.999 / 2

x = -0.0005 or x = -1.9995

Therefore, the solutions to the equation (0.1)^3 + 2x = (0.1)^2 - x^2 are x = -0.0005 and x = -1.9995.