Question

If using the method of completing the square to solve the quadratic equation x 2 + 14 x − 1 = 0 which number would have to be added to "complete the square"?

Answer 1

The values of x after solving the quadratic equation x²+14x-1 , using completing the square method is -√50-7 or +√50-7.

What is a quadratic equation?

A Quadratic equations is second-degree algebraic expressions and is of the form ax² + bx + c = 0.

Uisng the method of completing the square to solve the equation below, we following the steps.

Equation ⇒ x²+14x-1 = 0

Step 1:

Take the constant to the other side of the equation

• x²+14x = 1

Step 2:

Find half the coefficient of x, square, and  add it to both side of the equation.

• Coefficient of x = 14
• Half coefficient of x = 14/2 = 7
• square of half the coefficient of x = 7²

There,

• x²+14x+7² = 1+7²
• x²+14x+7² = 50

Step 3:

Express the trinomial on the left side as a square of binomial

• (x+7)² = 50

Step 4:

Take the square root of both side.

• √(x+7)² = √50
• x+7 = ±√50

Step 5:

Make x the subject of the equation by moving 7 to the other side of the equation

• x =  ±√50-7

Step 6:

Seperate the expression for each value of x

• Either x = -√50-7
• or x = +√50-7

Hence, the value of x is  -√50-7 or +√50-7.

Learn more about quadratic equation here: brainly.com/question/25841119

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