3x2-4x-15 = 0 (3x+5)(x-3) = 0 x = -5/3 or x = 3
Differentiate the function with respect to x: d/dx (x3 - 2x2 - 5x + 6) = 3x2 - 4x - 5 Set this derivative = 0 and solve. 3x2 - 4x - 5 = 0 implies that x = -0.7863 or 2.1196 (to 4 dp)
10x=x 9x=0 x=0
3x2 - 19x - 14 = 0 3x2 - 21x + 2x - 14 = 0 3x(x - 7) + 2(x - 7) = 0 (x - 7)(3x + 2) = 0 x - 7 = 0 or 3x + 2 = 0 x = 7 or x = -2/3
3x2 + 2x + 2 = 0 Can not be factored. You can however solve it for x: 3x2 + 2x = -2 x2 + 2x/3 = -2/3 x2 + 2x/3 + 1/9 = -2/3 + 1/9 (x + 1/9)2 = -5/9 x + 1/9 = ±√(-5/9) x = -1/9 ± i√(5/9) x = -1/9 ± i√5 / 3 x = -1/9 ± 3i√5 / 9 x = (-1 ± 3i√5) / 9
x=-.25.
3x2 + 17x + c = 0, rearranging gives c = -3x2 - 17x
-3x2 + 22x = 0 You start by dividing both sides by x: ∴ -3x + 22 = 0 Then rearrange to solve for x: ∴3x = 22 ∴ x = 7 + 1/3
3x2-9x = 0 x(3x-9) = 0 x = 0 or x = 3
Set the equation equal to zero. 3x2 - x = -1 3x2 - x + 1 = 0 The equation is quadratic, but can not be factored. Use the quadratic equation.
x4-8 = 0 x4 = 8 Eradicate the the power of 4 x = 1.681792831 Check: 1.6817928314 = 8.000000009 which is just about correct.
3x2 + 2x = 16 ∴ 3x2 + 2x - 16 = 0 ∴ 3x2 - 6x + 8x - 16 = 0 ∴ 3x(x - 2) + 8(x - 2) = 0 ∴ (3x + 8)(x - 2) = 0 ∴ x ∈ {-8/3, 2}
7
3x2 + x - 2 = 0(3x - 2) (x + 1) = 0x = + 2/3x = -1
Given the limitations of the browser that is used by this site, it is difficult to be certain about your question. If I misunderstand your question, (a) please accept my apologies and (b) resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared", "cubed" etc. I am assuming that you wish to solve e2x = 3x2 The only way that I can think of solving this is numerically and, in that case, the Newton Raphson method is quick and easy (for differentiable functions). To start with, your question is equivalent to finding a solution to e2x - 3x2 = 0, so define f(x) = e2x - 3x2. Therefore f'(x) = 2e2x - 6x. Start with x0 as the first guess. Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, … Continue until you get convergence of xn. If you plot a graph of f(x) against x, you will know that the root of f(x) lies between -1 and 0. This helps to select a suitable value for x0. If you start with -1, your error is around 8 per billion at x4. If you start with 0, it is less than 1 in 1.5 billion at x4. The answer is -0.390646381 (approx).
x = 0 or x = 2
3x2 + 10x - 8 = 0 3x2 + 12x - 2x - 8 = 0 3x(x + 4) - 2(x + 4) = 0 (3x - 2)(x + 4) = 0 So 3x - 2 = 0 or x + 4 = 0 so x = 2/3 or x = -4