Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve the quadratic equation [tex]\(x^2 + 12x - 11 = 0\)[/tex] by completing the square, follow these steps:
1. Start with the given equation:
[tex]\[ x^2 + 12x - 11 = 0 \][/tex]
2. Move the constant term to the right side of the equation:
[tex]\[ x^2 + 12x = 11 \][/tex]
3. Find the value that completes the square:
We need to add and subtract [tex]\(\left(\frac{b}{2}\right)^2\)[/tex] inside the equation, where [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex]. In this case, [tex]\(b = 12\)[/tex].
[tex]\[ \left(\frac{12}{2}\right)^2 = 6^2 = 36 \][/tex]
4. Add and subtract this value on the left side of the equation:
[tex]\[ x^2 + 12x + 36 - 36 = 11 \][/tex]
[tex]\[ x^2 + 12x + 36 = 47 \][/tex]
5. Rewrite the left side as a perfect square trinomial:
[tex]\[ (x + 6)^2 = 47 \][/tex]
6. Take the square root of both sides:
[tex]\[ x + 6 = \pm\sqrt{47} \][/tex]
7. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 \pm \sqrt{47} \][/tex]
8. Calculate the numerical values and round to three significant figures:
- The positive solution:
[tex]\[ x_1 = -6 + \sqrt{47} \approx 0.856 \][/tex]
- The negative solution:
[tex]\[ x_2 = -6 - \sqrt{47} \approx -12.856 \][/tex]
Therefore, the solutions to the equation [tex]\(x^2 + 12x - 11 = 0\)[/tex] are:
[tex]\[ x \approx 0.856 \quad \text{and} \quad x \approx -12.856 \][/tex]
rounded to three significant figures.
1. Start with the given equation:
[tex]\[ x^2 + 12x - 11 = 0 \][/tex]
2. Move the constant term to the right side of the equation:
[tex]\[ x^2 + 12x = 11 \][/tex]
3. Find the value that completes the square:
We need to add and subtract [tex]\(\left(\frac{b}{2}\right)^2\)[/tex] inside the equation, where [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex]. In this case, [tex]\(b = 12\)[/tex].
[tex]\[ \left(\frac{12}{2}\right)^2 = 6^2 = 36 \][/tex]
4. Add and subtract this value on the left side of the equation:
[tex]\[ x^2 + 12x + 36 - 36 = 11 \][/tex]
[tex]\[ x^2 + 12x + 36 = 47 \][/tex]
5. Rewrite the left side as a perfect square trinomial:
[tex]\[ (x + 6)^2 = 47 \][/tex]
6. Take the square root of both sides:
[tex]\[ x + 6 = \pm\sqrt{47} \][/tex]
7. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 \pm \sqrt{47} \][/tex]
8. Calculate the numerical values and round to three significant figures:
- The positive solution:
[tex]\[ x_1 = -6 + \sqrt{47} \approx 0.856 \][/tex]
- The negative solution:
[tex]\[ x_2 = -6 - \sqrt{47} \approx -12.856 \][/tex]
Therefore, the solutions to the equation [tex]\(x^2 + 12x - 11 = 0\)[/tex] are:
[tex]\[ x \approx 0.856 \quad \text{and} \quad x \approx -12.856 \][/tex]
rounded to three significant figures.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.