\[7{x}^{2}+10x+3=0\]

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Examples

Split the second term in

7{x}^{2}+10x+3

into two terms.

Multiply the coefficient of the first term by the constant term.

7\times 3=21

Ask: Which two numbers add up to

10

and multiply to

21

7

and

3

Split

10x

as the sum of

7x

and

3x

7{x}^{2}+7x+3x+3

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7{x}^{2}+7x+3x+3=0

Factor out common terms in the first two terms, then in the last two terms.

7x(x+1)+3(x+1)=0

Factor out the common term

x+1

(x+1)(7x+3)=0

Solve for

x

Ask: When will

(x+1)(7x+3)

equal zero?

When

x+1=0

7x+3=0

Solve each of the 2 equations above.

x=-1,-\frac{3}{7}

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x=-1,-\frac{3}{7}

Done

Decimal Form: -1, -0.428571

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