Solve for x. Enter the solutions from least to greatest. -2x^(2)-9=-107 lesser x= greater x=

Isolate x^2 term: First, we need to isolate the x^2 term by adding 107 to both sides of the equation. -2x^2 - 9 = -107 -2x^2 - 9 + 107 = -107 + 107 -2x^2 + 98 = 0Simplify the equation: Next, we need to simplify the equation by dividing all terms by -2 to make the x^2 coefficient positive. -2x^2 + 98 = 0 x^2 - 49 = 0Factor the equation: Now, we recognize that x^2 - 49 is a difference of squares, which can be factored as (x + 7)(x - 7). x^2 - 49 = (x + 7)(x - 7) = 0Set factors equal to zero: To find the solutions for x, we set each factor equal to zero and solve for x. x + 7 = 0 or x - 7 = 0Solve for x (equation 1): Solving the first equation for x gives us: x + 7 = 0 x = -7Solve for x (equation 2): Solving the second equation for x gives us: x - 7 = 0 x = 7Find the solutions for x: We have found two solutions for x. The lesser value is -7 and the greater value is 7. lesser x = -7 greater x = 7

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Solve for
x.
Enter the solutions from least to greatest.

-2x^(2)-9=-107
lesser
x=
greater
x=

Solve for $x$ . $\newline$ Enter the solutions from least to greatest. $\newline$ $-2 x^{2}-9=-107$ $\newline$ lesser $x=$ $\newline$ greater $x=$

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Math Problems

Algebra 1

Evaluate recursive formulas for sequences

Full solution

Q. Solve for

x

\newline

Enter the solutions from least to greatest.

\newline

-2 x^{2}-9=-107

\newline

lesser

x=

\newline

greater

x=

Isolate $x^2$ term: First, we need to isolate the $x^2$ term by adding $107$ to both sides of the equation. $\newline$ $-2x^2 - 9 = -107$ $\newline$ $-2x^2 - 9 + 107 = -107 + 107$ $\newline$ $-2x^2 + 98 = 0$
Simplify the equation: Next, we need to simplify the equation by dividing all terms by $-2$ to make the $x^2$ coefficient positive. $\newline$ $-2x^2 + 98 = 0$ $\newline$ $x^2 - 49 = 0$
Factor the equation: Now, we recognize that $x^2 - 49$ is a difference of squares, which can be factored as $(x + 7)(x - 7)$ . $\newline$ $x^2 - 49 = (x + 7)(x - 7) = 0$
Set factors equal to zero: To find the solutions for $x$ , we set each factor equal to zero and solve for $x$ . $x + 7 = 0$ or $x - 7 = 0$
Solve for x (equation $1$ ): Solving the first equation for x gives us: $\newline$ $x + 7 = 0$ $\newline$ $x = -7$
Solve for x (equation $2$ ): Solving the second equation for x gives us: $\newline$ $x - 7 = 0$ $\newline$ $x = 7$
Find the solutions for x: We have found two solutions for x. The lesser value is $-7$ and the greater value is $7$ . $\newline$ lesser $x = -7$ $\newline$ greater $x = 7$