Solve a quadratic equation by completing the square

Learning Objectives Identify the 'b' coefficient in a quadratic equation ax^2 + bx + c = 0 and use it to determine the term needed to create a perfect square trinomial. Transform a quadratic expression x^2 + bx into a perfect square trinomial by adding (b/2)^2. Rewrite a perfect square trinomial as the square of a binomial. Solve quadratic equations by completing the square when the leading coefficient 'a' is equal to 1. Solve quadratic equations by completing the square when the leading coefficient 'a' is not equal to 1. Apply the square root property to find all real or complex solutions to a quadratic equation. Derive the vertex form of a quadratic function, y = a(x-h)^2 + k, from the standard form using the completing the square method. Ho...

TermDefinitionExample Quadratic Equation (Standard Form)An equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and 'a' is not zero.2x^2 - 5x + 3 = 0 is a quadratic equation where a=2, b=-5, and c=3. Perfect Square TrinomialA trinomial that results from squaring a binomial. It has the form a^2 + 2ab + b^2 or a^2 - 2ab + b^2.x^2 + 10x + 25 is a perfect square trinomial because it can be factored into (x + 5)^2. BinomialA polynomial with exactly two terms, separated by a plus or minus sign.(x + 5) is a binomial. Leading CoefficientThe coefficient of the term with the highest degree in a polynomial. In a quadratic equation ax^2 + bx + c = 0, the leading coefficient is 'a'.In the equation 3x^2 + 7x - 2 = 0, the leading coefficient is...

The 'Completing the Square' Term c = (b/2)^2 To turn an expression x^2 + bx into a perfect square trinomial, you must add this specific value 'c'. First, identify the coefficient 'b' of the x-term. Then, divide it by 2 and square the result. Perfect Square Trinomial Factoring Pattern x^2 + bx + (b/2)^2 = (x + b/2)^2 Once you have created a perfect square trinomial, it can be factored into a binomial squared. The term inside the parenthesis is always 'x' plus half of the original 'b' coefficient. The Square Root Property If (expression)^2 = k, then expression = ±√k This is the final step in solving. Once you have an equation in the form of a squared binomial equal to a constant, you take the square root of both sides,...