Solve a quadratic equation by completing the square

Learning Objectives Identify the 'b' coefficient in a quadratic equation and calculate the value needed to create a perfect square trinomial. Transform a quadratic expression of the form x² + bx into a perfect square trinomial. Solve quadratic equations where the leading coefficient 'a' is 1 by completing the square. Solve quadratic equations where the leading coefficient 'a' is not 1 by completing the square. Apply the square root property correctly to find all possible real solutions. Explain the steps required to isolate the variable after creating a perfect square. Ever tried to fit a puzzle piece that's almost right? 🤔 Completing the square is like finding the exact missing piece to turn a complicated quadratic into a simple, perfect...

TermDefinitionExample Quadratic Equation (Standard Form)An equation that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.2x² - 5x + 3 = 0 is a quadratic equation where a=2, b=-5, and c=3. Perfect Square TrinomialA trinomial (an expression with three terms) that is the result of squaring a binomial. It can be factored into (x + k)² or (x - k)².x² + 10x + 25 is a perfect square trinomial because it can be factored as (x + 5)². CoefficientA number used to multiply a variable. In this topic, we are most interested in the 'b' coefficient, the number multiplying the x term.In the expression x² - 6x + 9, the coefficient 'b' is -6. Constant TermA term in an algebraic expression that does not contain any variables; its value is fixed.In ax...

The 'Completing the Square' Value c = (b/2)² To turn an expression like x² + bx into a perfect square trinomial, you must add a specific constant 'c'. This constant is found by taking the 'b' coefficient, dividing it by 2, and then squaring the result. Factoring a Perfect Square Trinomial x² + bx + (b/2)² = (x + b/2)² Once you have added the value (b/2)² to complete the square, the resulting trinomial can always be factored into a binomial squared. The term inside the parentheses is always 'x' plus half of the original 'b' coefficient. The Square Root Property Formula If X² = d, then X = ±√d This is the final step in solving. After you have an equation in the form (x + k)² = d, you take the square root of both sides....