What are the roots of the equation? $m^2+10=26$

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03-11-2026
Mathematics

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What are the roots of the equation? $m^2+10=26$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T19:55:50-05:00

Subtract 10 from both sides of the equation to isolate the $m^2$ term: $m^2 = 16$.
Apply the square root property to solve for $m$: $m = \pm\sqrt{16}$.
Evaluate the square roots: $m = 4$ and $m = -4$.
The final roots are $\boxed{4, -4}$.

Explanation

Analyzing the Equation

The given equation is $m^2 + 10 = 26$. We want to find the value or values of $m$ that satisfy this equation. This is a quadratic equation where we need to isolate the variable $m$. We start by subtracting $10$ from both sides of the equation to isolate the $m^2$ term.

Isolating the Variable and Simplifying

Subtracting $10$ from both sides:
\[m^2 = 26 - 10\]
\[m^2 = 16\]
Now that the equation is in the form $m^2 = 16$, we can solve for $m$ by taking the square root of both sides. Remember that the square root of a positive number yields both a positive and a negative root.

Calculating the Roots

By taking the square root of both sides, we have:
\[m = \pm \sqrt{16}\]
Since the square root of $16$ is $4$, the two solutions for $m$ are:
\[m = 4 \quad \text{or} \quad m = -4\]
Thus, the roots of the equation are $4$ and $-4$.

Examples

Quadratic equations often describe trajectories of objects under gravity. For example, if you are calculating at what time a ball thrown upwards reaches a certain height, the resulting motion equation can lead to a quadratic form. By finding the roots of such equations, you determine the specific time intervals when the object is at that height, which is essential for timing events accurately in physics or sports analysis.