Question

Solve for D


2d2+5d–12=0

Answer 1

Answer: d=3/2

Explanation:

Answer 2

`d = (3)/(2)`

`d = -4`

Explanation:

Given quadratic equation:

`2d^2 + 5d - 12 = 0`

To solve the given quadratic equation for d, we can use the method of factoring.

To factor a quadratic equation in the form ax² + bx + c = 0, first identity the coefficients a, b and c.

In the case of 2d² + 5d - 12 = 0:

• a = 2
• b = 5
• c = -12

Find two numbers that multiply to "ac" (in this case, 2 · (-12) = -24) and sum to "b" (which is 5).

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Among these, the factor pair that sums to 5 is -3 and 8.

Rewrite the middle term "b" using these two numbers:

`2d^2-3d+8d - 12 = 0`

Factor the first two terms and the last two terms separately:

`d(2d-3)+4(2d - 3) = 0`

Factor out the common term (2d - 3):

`(d+4)(2d-3)=0`

Apply the zero-product property by setting each factor equal to zero and solving for d:

`d+4=0 \implies d = -4`

`2d-3=0 \implies d=(3)/(2)`

Therefore, the solutions to the equation are:

`\large\boxed{\boxed{d = (3)/(2)\;\;\textsf{and}\;\;d = -4}}`