Solve quadratic equations

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HSA.REI.B.4

**HSA.REI.B.4**: Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

HSA.REI.B.4: Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

What you'll learn

Solve quadratic equations by inspection and by taking square roots when the equation is in the form (x - p)^2 = q
Use the method of completing the square to transform any quadratic equation ax^2 + bx + c = 0 into the form (x - p)^2 = q
Derive the quadratic formula from the completed-square form and apply it to solve any quadratic equation
Solve quadratic equations by factoring when the quadratic expression factors over the integers
Recognize when the discriminant (b^2 - 4ac) is negative and express the resulting complex solutions in the form a + bi

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Solving quadratic equations

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Quadratic formula complex solutions

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