how do I solve
-.2x^2+12x+11
Try using the quadratic formula.
Since it is not an equation, it cannot be solved. What does it =?
To solve the quadratic equation -.2x^2 + 12x + 11, you can follow these steps:
Step 1: Rewrite the equation in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients. In this case, the equation is already in this form.
Step 2: Identify the values of a, b, and c. For the equation -.2x^2 + 12x + 11, a = -.2, b = 12, and c = 11.
Step 3: Use the quadratic formula to find the solutions of the equation. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). Substitute the values of a, b, and c into the quadratic formula.
x = (-(12) ± √((12)^2 - 4*(-.2)*(11))) / (2*(-.2))
Simplifying the equation further, we get:
x = (-12 ± √(144 + 8.8)) / (-0.4)
x = (-12 ± √(152.8)) / (-0.4)
Step 4: Calculate the discriminant, which is the value inside the square root (√(b^2 - 4ac)) in the quadratic formula. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. And if it is negative, the equation has no real solutions.
The discriminant, D, is given by D = b^2 - 4ac. Substituting the values of a, b, and c into the formula:
D = (12)^2 - 4*(-.2)*(11)
D = 144 + 8.8
D = 152.8
Since the discriminant D is positive, there are two real solutions.
Step 5: Calculate the two solutions using the quadratic formula. Substitute the values of the discriminant, a, b, and c into the quadratic formula equation:
x = (-(-12) ± √(152.8)) / (-0.4)
Simplifying further:
x = (12 ± √(152.8)) / (-0.4)
Step 6: Calculate the solutions by evaluating the expression with the positive and negative sign:
x₁ = (12 + √(152.8)) / (-0.4)
x₂ = (12 - √(152.8)) / (-0.4)
Finally, use a calculator to approximate the solutions. The solutions of the equation -.2x^2 + 12x + 11 are x₁ ≈ -5.67 and x₂ ≈ 26.17.