Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
Sagot :
To solve the quadratic equation [tex]\(x^2 + 7x = 8\)[/tex], we first need to bring it to the standard form of [tex]\(ax^2 + bx + c = 0\)[/tex].
Starting with the given equation:
[tex]\[ x^2 + 7x = 8 \][/tex]
Subtract 8 from both sides to get:
[tex]\[ x^2 + 7x - 8 = 0 \][/tex]
Now, we need to solve for the roots of this quadratic equation. These roots are found using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In this equation, [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are:
[tex]\[ a = 1, \quad b = 7, \quad c = -8 \][/tex]
Substitute these values into the quadratic formula:
[tex]\[ x = \frac{-7 \pm \sqrt{7^2 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{-7 \pm \sqrt{49 + 32}}{2} \][/tex]
[tex]\[ x = \frac{-7 \pm \sqrt{81}}{2} \][/tex]
[tex]\[ x = \frac{-7 \pm 9}{2} \][/tex]
This gives us two solutions:
1. When we use the positive square root:
[tex]\[ x = \frac{-7 + 9}{2} \][/tex]
[tex]\[ x = \frac{2}{2} \][/tex]
[tex]\[ x = 1 \][/tex]
2. When we use the negative square root:
[tex]\[ x = \frac{-7 - 9}{2} \][/tex]
[tex]\[ x = \frac{-16}{2} \][/tex]
[tex]\[ x = -8 \][/tex]
Thus, the solutions to the equation are:
[tex]\[ x = 1 \quad \text{and} \quad x = -8 \][/tex]
Looking at the given options, we find that the pair of solutions matches option C.
Therefore, the correct answer is:
C. [tex]\( x = 1 ; x = -8 \)[/tex]
Starting with the given equation:
[tex]\[ x^2 + 7x = 8 \][/tex]
Subtract 8 from both sides to get:
[tex]\[ x^2 + 7x - 8 = 0 \][/tex]
Now, we need to solve for the roots of this quadratic equation. These roots are found using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In this equation, [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are:
[tex]\[ a = 1, \quad b = 7, \quad c = -8 \][/tex]
Substitute these values into the quadratic formula:
[tex]\[ x = \frac{-7 \pm \sqrt{7^2 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{-7 \pm \sqrt{49 + 32}}{2} \][/tex]
[tex]\[ x = \frac{-7 \pm \sqrt{81}}{2} \][/tex]
[tex]\[ x = \frac{-7 \pm 9}{2} \][/tex]
This gives us two solutions:
1. When we use the positive square root:
[tex]\[ x = \frac{-7 + 9}{2} \][/tex]
[tex]\[ x = \frac{2}{2} \][/tex]
[tex]\[ x = 1 \][/tex]
2. When we use the negative square root:
[tex]\[ x = \frac{-7 - 9}{2} \][/tex]
[tex]\[ x = \frac{-16}{2} \][/tex]
[tex]\[ x = -8 \][/tex]
Thus, the solutions to the equation are:
[tex]\[ x = 1 \quad \text{and} \quad x = -8 \][/tex]
Looking at the given options, we find that the pair of solutions matches option C.
Therefore, the correct answer is:
C. [tex]\( x = 1 ; x = -8 \)[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.