Math Problem Statement

please slve

Solution

Let's solve the quadratic equation x2+2x6=0x^2 + 2x - 6 = 0 by completing the square.

Step-by-Step Solution:

  1. Start with the quadratic equation: x2+2x6=0x^2 + 2x - 6 = 0

  2. Move the constant term to the right side: x2+2x=6x^2 + 2x = 6

  3. To complete the square, take half of the coefficient of xx (which is 2), square it, and add it to both sides: (22)2=1\left(\frac{2}{2}\right)^2 = 1 Add 1 to both sides: x2+2x+1=6+1x^2 + 2x + 1 = 6 + 1

  4. Now the left side is a perfect square: (x+1)2=7(x + 1)^2 = 7

  5. Take the square root of both sides: x+1=±7x + 1 = \pm \sqrt{7}

  6. Solve for xx: x=1±7x = -1 \pm \sqrt{7}

Final Answer:

x=1+7,x=17x = -1 + \sqrt{7}, \quad x = -1 - \sqrt{7}

To round to the nearest hundredth:

  • 72.65\sqrt{7} \approx 2.65

So:

  • x11+2.65=1.65x_1 \approx -1 + 2.65 = 1.65
  • x212.65=3.65x_2 \approx -1 - 2.65 = -3.65

Final Answer Rounded to Nearest Hundredth:

x1.65,3.65x \approx 1.65, -3.65

Would you like further details on this solution or have any questions?

Related Questions:

  1. How do you solve quadratic equations using the quadratic formula?
  2. What are the conditions under which a quadratic equation has real, repeated, or complex solutions?
  3. How can you graphically represent the solutions of a quadratic equation?
  4. What is the importance of completing the square in deriving the quadratic formula?
  5. How does completing the square help in converting a quadratic equation into vertex form?

Tip:

Completing the square is a useful technique not only for solving quadratic equations but also for deriving the quadratic formula and finding the vertex of a parabola.

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Completing the Square

Formulas

Quadratic formula

Theorems

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Suitable Grade Level

Grades 9-12