Are you struggling to find the solutions to 4x^2-5x-12=0? Look no further! In this solution, we’ll guide you step-by-step through the process of solving the quadratic equation 4x^2 – 5x – 12 = 0 using the quadratic formula. Get ready to discover the exact solutions to this equation and impress your math teacher with your newfound skills!
Solve Using Quadratic Equation
To solve the quadratic equation 4x^2 – 5x – 12 = 0, you can use the quadratic formula:
x = (-b ± √(b^2 – 4ac)) / 2a
where a = 4, b = -5, and c = -12.
Substituting these values into the formula, we get:
x = (-(-5) ± √((-5)^2 – 4(4)(-12))) / 2(4)
Simplifying this expression:
x = (5 ± √(25 + 192)) / 8
x = (5 ± √217) / 8
So the solutions to the equation are:
x = (5 + √217) / 8
or
x = (5 – √217) / 8
These are the exact solutions to the equation. If you need decimal approximations, you can use a calculator to evaluate the square root of 217 and simplify the fractions.
Another Solution to Solve For X
Explanation – 4x^2-5x-12=0
Here’s a step-by-step explanation of how to solve the quadratic equation 4x^2 – 5x – 12 = 0 using the quadratic formula:
Step 1: Identify the values of a, b, and c in the quadratic equation.
In the equation 4x^2 – 5x – 12 = 0, the coefficient of x^2 is 4, the coefficient of x is -5, and the constant term is -12. So, we have:
a = 4 b = -5 c = -12
Step 2: Substitute the values of a, b, and c into the quadratic formula.
The quadratic formula is:
x = (-b ± √(b^2 – 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-(-5) ± √((-5)^2 – 4(4)(-12))) / 2(4)
Step 3: Simplify the expression under the square root sign.
Simplifying the expression under the square root sign, we get:
√((-5)^2 – 4(4)(-12)) = √(25 + 192) = √217
Step 4: Simplify the expression inside the parentheses.
Simplifying the expression inside the parentheses, we get:
x = (5 ± √217) / 8
These are the exact solutions to the quadratic equation 4x^2 – 5x – 12 = 0. If you need decimal approximations, you can use a calculator to evaluate the square root of 217 and simplify the fractions.
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