Problemas
If using the method of completing the square to solve the quadratic equation x^2+14x+34=0 , which number would have to be added to "complete the square"? Answer Attemptiout of 2
Roztwór
Marcelo
maestro · Tutor durante 5 años
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(323 Votos)
Respuesta
The number that completes the square is 49.
Explicación
## Step 1The method of completing the square is a technique used to solve quadratic equations. The general form of a quadratic equation is
. The method involves rearranging the equation into a perfect square trinomial on one side of the equation.## Step 2In the given equation
, we need to find the number that completes the square. This is done by taking half of the coefficient of the x term (which is 14), squaring it, and then adding it to the equation.### **The formula to find the number that completes the square is \( \left(\frac{b}{2}\right)^2 \)**## Step 3Substitute the coefficient of x (which is 14) into the formula.### **So, \( \left(\frac{14}{2}\right)^2 = 49 \)**