Personal Math Assistant Your Math Genius

Sure, I can help you solve the equation 0.1x^4 - 1.3x^2 + 3.6 = 0. To solve for x, we will use the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by: x = (-b ± sqrt(b^2 - 4ac)) / 2a However, the equation given is not quadratic. It is a quartic equation, meaning it has a degree of four. To solve it, we can use a technique called substitution. Let's substitute a variable u for x^2. Then our equation becomes: 0.1u^2 - 1.3u + 3.6 = 0 Now we can use the quadratic formula to solve for u: u = (-(-1.3) ± sqrt((-1.3)^2 - 4(0.1)(3.6))) / 2(0.1) Simplifying the expression under the square root, we get: u = (1.3 ± sqrt(1.69 - 1.44)) / 0.2 u = (1.3 ± sqrt(0.25)) / 0.2 u = (1.3 ± 0.5) / 0.2 So we have two possible solutions for u: u1 = 9 u2 = 2 Now we can substitute back to solve for x: For u1: u1 = x^2 x^2 = 9 x = ±3 For u2: u2 = x^2 x^2 = 2 x = ±sqrt(2) Therefore, the solutions to the original equation 0.1x^4 - 1.3x^2 + 3.6 = 0 are: x = 3, -3, sqrt(2), -sqrt(2). I hope this helps! Let me know if you have any questions.