Solve. For x
1. 3x^2-6=0
2. 1/x (6x^3+5x^2)=21
3. x/2+6=-10/x
4. 2x^2=14x
x^2 = 2
x = +/- sqrt 2
2. not sure what is denominator
3. x^2/2 + 6 x + 10 = 0
x^2 + 12 x + 20 = 0
(x+10)(x+2) = 0
x = -10 or x = -2
4. x^2 - 7 x = 0
x (x-7) = 0
x = 0 or x = 7
Thanks damon
Thanks damon but I don't understand what did you on number 3???
Sure! I can help you solve these equations.
1. To solve the equation 3x^2 - 6 = 0, we can use the quadratic formula. The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the equation in the form ax^2 + bx + c = 0. In this case, a = 3, b = 0, and c = -6. Plugging these values into the formula, we have x = (0 ± √(0^2 - 4(3)(-6))) / (2(3)). Simplifying further, we get x = ±√(0 + 72) / 6. This simplifies to x = ±√72 / 6. Finally, we can simplify this further to get x = ±√12 / 2 or x = ±√3.
2. To solve the equation (1/x) (6x^3 + 5x^2) = 21, we can start by multiplying both sides of the equation by x to get rid of the fraction. This gives us 6x^3 + 5x^2 = 21x. Next, we can rearrange the equation to get 6x^3 + 5x^2 - 21x = 0. Now, we have a cubic equation, which can be difficult to solve directly. One approach is to factor the equation or use numerical methods to approximate the solution. In this case, factoring the equation may not be straightforward, so we can use numerical methods like graphing or Newton's method to find the solution.
3. To solve the equation x/2 + 6 = -10/x, we can start by multiplying both sides of the equation by 2x to eliminate the fractions. This yields x^2 + 12x + 20 = 0. This is a quadratic equation which can be solved by factoring or by using the quadratic formula. Factoring this equation gives us (x + 2)(x + 10) = 0. Thus, we have two possible solutions: x = -2 and x = -10.
4. To solve the equation 2x^2 = 14x, we can start by subtracting 14x from both sides to bring all the terms to one side of the equation. This gives us 2x^2 - 14x = 0. We can now factor out 2x to get 2x(x - 7) = 0. By using the zero product property, we know that either 2x = 0 or x - 7 = 0. Simplifying these equations, we find that x = 0 or x = 7. So, the solutions to the equation are x = 0 and x = 7.