Questions: Resolver la ecuación cuadrática completando el cuadrado. x^2-6 x+3=0 Forma: ( x + ) ^ 2 = ( x - - ) ^ 2 = Solución: x=

Transcript text: Resolver la ecuación cuadrática completando el cuadrado. \[ x^{2}-6 x+3=0 \] Forma: ( x + \square ) ^ { 2 } = \square ( x - - \square ) ^ { 2 } = \square Solución: \[ x=\square \]

Solution

Solution Steps

Step 1: Rewrite the equation in standard form

The given quadratic equation is: \[ x^2 - 6x + 3 = 0 \]

Step 2: Move the constant term to the other side

To complete the square, we first move the constant term to the other side of the equation: \[ x^2 - 6x = -3 \]

Step 3: Complete the square

To complete the square, we need to add and subtract the square of half the coefficient of \(x\) on the left side. The coefficient of \(x\) is -6, so half of it is -3, and its square is 9: \[ x^2 - 6x + 9 = -3 + 9 \] \[ (x - 3)^2 = 6 \]

Step 4: Solve for \(x\)

Now, take the square root of both sides: \[ x - 3 = \pm \sqrt{6} \] \[ x = 3 \pm \sqrt{6} \]