16x^2+4x^x-1-12=0
The equation you provided, 16x^2 + 4x^x - 1 - 12 = 0, seems to have a typographical mistake. The term "x^x" is unusual and likely incorrect. It is possible that you meant to write "x" instead of "x^x".
Assuming that the equation is 16x^2 + 4x - 1 - 12 = 0, we can solve it by following these steps:
Step 1: Simplify the equation by combining like terms. The equation becomes 16x^2 + 4x - 13 = 0.
Step 2: To solve a quadratic equation like this, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case, a = 16, b = 4, and c = -13. Let's substitute these values into the formula:
x = (-(4) ± √((4)^2 - 4(16)(-13))) / (2(16))
Step 3: Calculate the discriminant, which is the value inside the square root: b^2 - 4ac.
Discriminant = (4)^2 - 4(16)(-13)
Discriminant = 16 + 832
Discriminant = 848
Step 4: Substitute the discriminant into the quadratic formula:
x = (-(4) ± √(848)) / (2(16))
Step 5: Simplify the equation and continue solving:
x = (-4 ± √848) / 32
Step 6: Calculate the square root of 848:
√848 = 29.1 (approximately)
Step 7: Substitute this value back into the equation:
x = (-4 ± 29.1) / 32
Step 8: Solve for both possible values of x:
x1 = (-4 + 29.1) / 32 ≈ 0.875
x2 = (-4 - 29.1) / 32 ≈ -1.125
Therefore, the solutions to the equation 16x^2 + 4x - 13 = 0 are approximately x = 0.875 and x = -1.125.