completing the square solved examples Example 1 Solve the quadratic equation below using the method of completing the square Move the constant to the right side of the equation while keeping the latex x latex terms on the left I can do that by subtracting both sides by latex 14 latex Next identify the coefficient of the linear term just the latex x latex term which is
Step 1 Write the quadratic equation as x 2 bx c Coefficient of x 2 needs to be 1 If not take it as the common factor Step 2 Determine half of the coefficient of x Step 3 Take the square of the number obtained in step 1 Step 4 Add and subtract the square obtained in step 2 to the x 2 term Step 1 can be skipped in this example since the coefficient of x 2 is 1 Step 2 Move the number term to the right side of the equation x 2 4x 1 Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation b 2 2 4 2 2 2 2 4
completing the square solved examples
completing the square solved examples
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Question Video Solving Quadratic Equations By Completing The Square
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Solving Quadratic Equations More Completing The Square Examples 2
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Howto Complete a Square of x2 bx x 2 b x Identify b b the coefficient of x x Find 12b 2 1 2 b 2 the number to complete the square Add the 12b 2 1 2 b 2 to x2 bx x 2 b x Factor the perfect square trinomial writing it as a binomial squared 1 Subtract 57 from both sides which will give you x squared 16x 57 2 Complete the square x squared 16x 64 7 3 Factor the left side of the equation x 8 squared 7 4 Square root both sides of the equation x 8 positive or negative square root of 7 5 Split the equations into x 8 positive square root of 7 and x 8 negative
However even if an expression isn t a perfect square we can turn it into one by adding a constant number For example x 6x 5 isn t a perfect square but if we add 4 we get x 3 This in essence is the method of completing the square Created by Sal Khan and CK 12 Foundation Questions Tips Thanks Key Steps in Solving Quadratic Equation by Completing the Square 1 Keep all the latex x latex terms both the squared and linear on the left side while moving the constant to the right side In symbol rewrite the general form latex a x 2 bx c latex as latex a x 2 bx c latex
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Solve by completing the square x2 14x 46 0 Solution Step 1 Add or subtract the constant term to obtain the equation in the form x2 bx c In this example subtract 46 to move it to the right side of the equation Step 2 Use b 2 2 to determine the value that completes the square Here b 14 Solve by completing the square 2 x 2 5 x 1 0 Solution Notice that the leading coefficient is 2 Therefore divide both sides by 2 before beginning the steps required to solve by completing the square
To complete the square you need to have all of the constants numbers that are not attached to variables on the right side of the equals sign In this example you can achieve this by subtracting 9 from both sides and simplifying as follows By completing the square let us solve the quadratic equation x 2 4x 1 0 Step 1 Here this step is not needed as a 1 Step 2 Moving the constant term to the right side of the equation x 2 4x 1 Step 3 Adding the square of half the coefficient of the x term to both sides of the equation
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completing the square solved examples - Key Steps in Solving Quadratic Equation by Completing the Square 1 Keep all the latex x latex terms both the squared and linear on the left side while moving the constant to the right side In symbol rewrite the general form latex a x 2 bx c latex as latex a x 2 bx c latex