1Cademy - Solving $$5m^2 = 80$$ Using the Square Root Property

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How to Solve a Quadratic Equation Using the Square Root Property

Example

Solving $5m^2 = 80$ Using the Square Root Property

Solve $5m^2 = 80$ by applying the four-step procedure for the Square Root Property. This equation has a coefficient of $5$ on the squared term that must be removed before the property can be applied.

Step 1 — Isolate the quadratic term and make its coefficient one. The quadratic term $5m^2$ is already alone on one side, but its coefficient is $5$ , not $1$ . Divide both sides by $5$ :

$\frac{5m^2}{5} = \frac{80}{5}$

$m^2 = 16$

Step 2 — Apply the Square Root Property:

$m = \pm\sqrt{16}$

Step 3 — Simplify the radical. Since $16$ is a perfect square ( $4^2 = 16$ ):

$m = \pm 4$

Rewrite to show two solutions: $m = 4$ or $m = -4$ .

Step 4 — Check both solutions by substituting into the original equation:

For $m = 4$ : $5(4)^2 = 5 \cdot 16 = 80$ ✓

For $m = -4$ : $5(-4)^2 = 5 \cdot 16 = 80$ ✓

The solutions are $m = 4$ and $m = -4$ . This example demonstrates Step 1 of the procedure: when the squared variable has a coefficient other than $1$ , dividing both sides by that coefficient reduces the equation to the form $x^2 = k$ so the Square Root Property can be applied.

Updated 2026-04-21

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OpenStax Elementary Algebra

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