4x ^ 2 – 5x – 12 = 0

Solve: 4x ^ 2 – 5x – 12 = 0

To solve the equation 4x^2 – 5x – 12 = 0, we can use the quadratic formula, which gives:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
Here, a = 4, b = -5, and c = -12, so substituting these values, we get:
x = (-(-5) ± sqrt((-5)^2 – 4(4)(-12))) / 2(4)
Simplifying the expression under the square root, we get:
x = (5 ± sqrt(25 + 192)) / 8
x = (5 ± sqrt(217)) / 8
Therefore, the solutions to the equation 4x^2 – 5x – 12 = 0 are:
x = (5 + sqrt(217)) / 8
x = (5 – sqrt(217)) / 8
So, x can be approximated to:
x ≈ 2.25 or x ≈ -1.75
Hence, the solutions to the equation are x ≈ 2.25 and x ≈ -1.75.

Solve: x + 9 = 18 + -2x

To solve the equation x + 9 = 18 – 2x, we can first simplify it by adding 2x to both sides, which gives:
x + 2x + 9 = 18
Combining like terms, we get:
3x + 9 = 18
Next, we can isolate x on one side by subtracting 9 from both sides, which gives:
3x = 9
Finally, we can solve for x by dividing both sides by 3, which gives:
x = 3
Therefore, the solution to the equation x + 9 = 18 – 2x is x = 3.

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