Solve the following quadratic equation. 2x 2 −x−15=0

Sure, let's solve the quadratic equation step by step.

The given quadratic equation is 2x^2 - x - 15 = 0.

Step 1: Identify the coefficients a, b, and c in the equation ax^2 + bx + c = 0. Here, a = 2, b = -1, and c = -15.

Step 2: Use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / 2a.

Step 3: Substitute the values of a, b, and c into the formula.

x = [1 ± sqrt((-1)^2 - 42(-15))] / 2*2 x = [1 ± sqrt(1 + 120)] / 4 x = [1 ± sqrt(121)] / 4 x = [1 ± 11] / 4

Step 4: Solve for x.

x = (1 + 11) / 4 = 3 x = (1 - 11) / 4 = -2.5

So, the solutions to the equation 2x^2 - x - 15 = 0 are x = 3 and x = -2.5.

Sure, let's solve the quadratic equation step by step.

The given quadratic equation is 2x^2 - x - 15 = 0.

Step 1: Write down the equation. 2x^2 - x - 15 = 0

Step 2: Factor the quadratic equation. This involves finding two numbers that multiply to give the product of the coefficient of x^2 term (which is 2) and the constant term (which is -15), and add up to give the coefficient of x term (which is -1).

The two numbers that satisfy these conditions are -5 and 3 because (-5) * 3 = -15 and -5 + 3 = -1.

So, we can write the equation as: 2x^2 - 5x + 3x - 15 = 0

Step 3: Group the terms and factor by grouping. This gives us: x(2x - 5) + 3(2x - 5) = 0

Step 4: Notice that (2x - 5) is a common factor. So, we can write the equation as: (2x - 5)(x + 3) = 0

Step 5: Set each factor equal to zero and solve for x. This gives us: 2x - 5 = 0 => 2x = 5 => x = 5/2 = 2.5 and x + 3 = 0 => x = -3

So, the solutions to the equation 2x^2 - x - 15 = 0 are x = 2.5 and x = -3.