Please solve for x. ax^2 + bx +c=0
the statement of the quadratic formula would be the solution
x = (-b ± √(b^2 - 4ac)/(2a)
x = [-b �} �ã(b^2 - 4ac)]/(2a)
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To solve for x in the quadratic equation ax^2 + bx + c = 0, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here's how you can find the solution using the quadratic formula:
Step 1: Identify the values of a, b, and c from the given equation ax^2 + bx + c = 0.
Step 2: Substitute the values of a, b, and c into the quadratic formula.
Step 3: Simplify the expression inside the square root.
Step 4: Calculate the values for x using the numerator and denominator of the quadratic formula separately for both the positive and negative solutions.
Let's go through an example to illustrate the process:
Example: Solve the equation 2x^2 + 5x - 3 = 0.
Step 1: Identify the values of a, b, and c:
- a = 2
- b = 5
- c = -3
Step 2: Substitute the values into the quadratic formula:
x = (-5 ± √(5^2 - 4(2)(-3))) / (2(2))
Step 3: Simplify the expression inside the square root:
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √(49)) / 4
x = (-5 ± 7) / 4
Step 4: Calculate the values for x:
x1 = (-5 + 7) / 4 = 2 / 4 = 1/2
x2 = (-5 - 7) / 4 = -12 / 4 = -3
Therefore, the solutions for the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.