Introduction: How to Solve a Quadratic Equation
*Things to Know Before Getting Started:
Materials Needed: Paper, pencil, calculator
PEMDAS: PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third, etc. until the calculation is complete.
Coefficient: a number placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).
**It may occur that one’s answer inside the square root box is negative. If this happens, your answer will be undefined.
Step 1: Set Equation Equal to Zero
Solve 6x^2 + 11x = 35.
To successfully solve a quadratic equation, all variables (expressions whose value we don’t know) and constants (simply put, numbers) must be on the same side of the equation. Therefore the equation is equal to 0.
EX. 6x^2 + 11x - 35 = 0
Step 2: Identify the Coefficients
Once your equation is equal to 0, identify the “a,” “b,” and “c” variables according to the ax^2 + bx + c = 0 template.
Your a variable will be the coefficient* of the x^2 variable. Your b variable will be the coefficient of x^1 variable. Your c variable will simply be the constant.
Step 3: Plugging in Values
The quadratic formula is in one of the pictures.
Although the formula may look intimidating, it is important to remember that in this step all we’re doing is plugging in the values for a, b, and c in the corresponding location.
Step 4: Simplifying Expressions
Following the order of operations (PEMDAS)*, SIMPLIFY the equation. Begin with the expressions inside the parentheses.
Step 5: Replace Expression
REPLACE the expressions in parentheses with the equal constant you calculated in Step 4.
Step 6: Exponents
Continue to simplify the equation by following the order of operations. Now you will simplify the expression with exponents.
Step 7: Replace Exponential Expression
REPLACE the exponential expression with its equal constant you calculated in Step 6.
Step 8: Multiplication
Continue to simplify the equation by following the order of operations. Now you will simplify the expressions with multiplication.
Step 9: Replace Multiplication Expression
REPLACE the multiplicative expression with its equal constant you calculated in Step 8.
Step 10: Addition
Continue to simplify the equation by following the order of operations. Now you will simplify the expression with addition.
Step 11: Replace Addition Expression
REPLACE the addition expression with its equal constant you calculated in Step 10.
Step 12: Square Root
SIMPLIFY the square root.
Step 13: Replace Square Root Expression
REPLACE the expression with square root with its equal constant you calculated in Step 12.
Step 14: Separate Two Equations
Separate the equation into TWO equations due to the plus/minus sign. One will keep only the plus sign, one will only keep the minus sign.
Step 15: Simplify
Simplify the addition/subtraction expressions.
Step 16: Replaces Expressions
REPLACE the addition/subtraction expression with the equal calculated constants from Step 15.
Step 17: Simplify Answer
Simplify your two fractions. This will ultimately yield the two x values that make the quadratic equation true! :)