IDNLearn.com makes it easy to find answers and share knowledge with others. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

What are the solutions to this equation?

[tex]\(2x^2 = -10x + 12\)[/tex]

A. [tex]\(x = -3\)[/tex]
B. [tex]\(x = 1\)[/tex]
C. [tex]\(x = 3\)[/tex]
D. [tex]\(x = 6\)[/tex]
E. [tex]\(x = -2\)[/tex]
F. [tex]\(x = -6\)[/tex]


Sagot :

To find the solutions to the equation [tex]\(2x^2 = -10x + 12\)[/tex], we first need to rewrite it in standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex]. Here are the steps:

1. Starting with the equation:
[tex]\[ 2x^2 = -10x + 12 \][/tex]

2. Bring all terms to one side to set the equation to zero:
[tex]\[ 2x^2 + 10x - 12 = 0 \][/tex]

Now we have a standard form quadratic equation:
[tex]\[ 2x^2 + 10x - 12 = 0 \][/tex]

The next step is to solve this quadratic equation, either by factoring, completing the square, or using the quadratic formula. The typical quadratic formula is given by:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 2 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = -12 \)[/tex].

However, knowing the results directly, we see the solutions to the equation [tex]\(2x^2 + 10x - 12 = 0\)[/tex] are:

[tex]\[ x = -6 \quad \text{and} \quad x = 1 \][/tex]

Thus, the solutions to the given quadratic equation [tex]\(2x^2 + 10x - 12 = 0 \)[/tex] are:

[tex]\[ x = -6 \quad \text{and} \quad x = 1 \][/tex]

Among the options given:
[tex]\[ x = -3, x = 1, x = 3, x = 6, x = -2, x = -6 \][/tex]
the correct solutions are:
[tex]\[ x = -6 \quad \text{and} \quad x = 1 \][/tex]