Solve the following quadratic equations. 2 x 2 − 10 x = 0 2x^2-10x=0

Here, we've been asked to solve this quadratic equation, and to do that we're going to use some of our factoring techniques. So the first thing I notice with this quadratic is that each of the terms is even, which means that they both share a factor of two. They also both share a factor of x as they both contain at least one x variable. So that tells me that my GCF for these two terms is two x, and I can first factor that out. So factoring out 2x, we're left with x minus five. And now I can apply my zero product property to this new factored form of the polynomial. So when does it 2x equals zero, and when does x minus five equals zero? Well, 2x equals zero when x equals zero. And x minus five equals zero when x equals five. So these are the two solutions to my equation, and I can always check my work by taking these values and plugging them back into my polynomial to make sure that the equation is true.

Solve the following quadratic equations. 2 x 2 − 10 x = 0 2x^2-10x=0

x = 0 x=0 x = 0 or x = − 5 x=-5

7. Factoring

Quadratic Equations & Applications

Beginning Algebra

7. Factoring

Quadratic Equations & Applications

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Multiple Choice

Solve the following quadratic equations.
$2 x^{2} - 10 x = 0$

$x=0$ or $x = - 5$

$x equals 2$ or $x = - 5$

$x equals 0$ or $x equals 5$

$x equals 0$ or $x equals 10$

Verified step by step guidance

Start with the given quadratic equation: \$2x^2 - 10x = 0$.

Factor out the greatest common factor (GCF) from both terms on the left side. The GCF is \$2x$, so rewrite the equation as $2x(x - 5) = 0$.

Apply the Zero Product Property, which states that if a product of two factors equals zero, then at least one of the factors must be zero. Set each factor equal to zero: \$2x = 0$ and $x - 5 = 0$.

Solve each equation separately: from \$2x = 0$, divide both sides by 2 to get $x = 0$; from $x - 5 = 0$, add 5 to both sides to get $x = 5$.

Write the solution set as $x = 0$ or $x = 5$, which are the values of $x$ that satisfy the original equation.

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Solve the following quadratic equations.
$2 x^{2} - 10 x = 0$