$solve quadratic equation by completing the square$

Binomial Coefficients and the Binomial Theorem.Quiz: Definition and Examples of Sequences.Quiz: Exponential and Logarithmic Equations.Systems of Inequalities Solved Graphically.Quiz: Systems of Equations Solved Graphically.Systems of Equations Solved Graphically.Quiz: Systems of Equations Solved Algebraically.Systems of Equations Solved Algebraically.Quiz: Solving Equations in Quadratic Form.Quiz: Solving Quadratics by the Quadratic Formula.Solving Quadratics by the Quadratic Formula.Quiz: Solving Quadratics by Completing the Square.Solving Quadratics by Completing the Square.Quiz: Solving Quadratics by the Square Root Property.Solving Quadratics by the Square Root Property.Quiz: Adding and Subtracting Radical Expressions.Adding and Subtracting Radical Expressions.Quiz: Proportion, Direct Variation, Inverse Variation, Joint Variation.Proportion, Direct Variation, Inverse Variation, Joint Variation.Quiz: Adding and Subtracting Rational Expressions.Adding and Subtracting Rational Expressions.Quiz: Trinomials of the Form ax^2 + bx + c.Quiz: Trinomials of the Form x^2 + bx + c.Quiz: Adding and Subtracting Polynomials.Quiz: Linear Equations: Solutions Using Determinants with Three Variables.Linear Equations: Solutions Using Determinants with Three Variables.Quiz: Linear Equations: Solutions Using Matrices with Three Variables.Linear Equations: Solutions Using Matrices with Three Variables.Linear Equations: Solutions Using Elimination with Three Variables.

Quiz: Linear Equations: Solutions Using Elimination with Three Variables.

Quiz: Linear Inequalities: Solutions Using Graphing with Two Variables.

Linear Inequalities: Solutions Using Graphing with Two Variables.

Quiz: Linear Equations: Solutions Using Determinants with Two Variables.

Linear Equations: Solutions Using Determinants with Two Variables.

Quiz: Linear Equations: Solutions Using Matrices with Two Variables.

Linear Equations: Solutions Using Matrices with Two Variables.

Quiz: Linear Equations: Solutions Using Elimination with Two Variables.

Linear Equations: Solutions Using Elimination with Two Variables.

Quiz: Linear Equations: Solutions Using Substitution with Two Variables.

Linear Equations: Solutions Using Substitution with Two Variables.

Quiz: Linear Equations: Solutions Using Graphing with Two Variables.

Linear Equations: Solutions Using Graphing with Two Variables.

Quiz: Slopes of Parallel and Perpendicular Lines.

Slopes of Parallel and Perpendicular Lines.

Note that if b = 0, then (b/2)² = 0, and so we would add 0 to both sides of the equations. If b=0, then you may skip Steps 2, 3, and 4 and go from x² = -c (Step 1) directly to x = ±√|c| (Step 5).īecause in Step 2, we take b and perform some arithmetic operations on it, which gives us the number with which we will 'complete the square.' Now just go ahead with the steps we explained in the example above.

Dividing either side by 2, we obtainĪnd so the coefficient in front of x² is equal to 1. transform the problem to some you've already solved🙃 What does that mean in our context? Just divide your equation by a!īy completing the square. What do you do if you are asked to solve a quadratic equation where a ≠ 1? Just apply one of the most frequently used problem-solving techniques in math, namely. In the example above, it is important that the coefficient in front of x² is equal to 1. This means we've determined the points where the parabola y = x² + 6x - 7 intersects the x-axis. Hence, we've found the solutions of x² + 6x - 7 = 0. Recall the short multiplication formula, (p + q)² = p² + 2pq + q², and note that we may apply it 'backwards' to the left-hand side of our equation (with p = x and q = 3). Now it's time to complete the square! Take one-half of the coefficient in front of x and square it:Īdd the number computed in Step 2 to both sides of the equation: We break the process into several simple steps so that nobody gets overwhelmed by the formula for completing the square:Īdd 7 to either side of the equation so that the left-hand side contains only terms with x:

Solve quadratic equation by completing the square