Solve for x. Enter the solutions from least to greatest. 5x^(2)+15 x-140=0 lesser x= greater x=

Factor Quadratic Equation: First, we need to factor the quadratic equation 5x^2 + 15x - 140 = 0. We look for two numbers that multiply to 5*(-140) = -700 and add up to 15. The numbers that satisfy these conditions are 35 and -20. So we can rewrite the equation as 5x^2 + 35x - 20x - 140 = 0.Factor by Grouping: Next, we factor by grouping. We group the terms as follows: (5x^2 + 35x) - (20x + 140) = 0. Then we factor out the common factors in each group: 5x(x + 7) - 20(x + 7) = 0.Factor Common Binomial: Now we can factor out the common binomial factor (x + 7): (5x - 20)(x + 7) = 0.Apply Zero Product Property: We now have the product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero: 5x - 20 = 0 and x + 7 = 0.Solve for x: Solving the first equation 5x - 20 = 0 for x gives us: 5x = 20 x = 20/5 x = 4.Final Solutions: Solving the second equation x + 7 = 0 for x gives us: x = -7.We have found two solutions: x = 4 and x = -7. To answer the question prompt, we order them from least to greatest: lesser x = -7 greater x = 4.

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

5x^(2)+15 x-140=0
lesser
x=
greater
x=

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $5 x^{2}+15 x-140=0$ $\newline$ lesser $x=$ $\newline$ greater $x=$

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Precalculus

Solve logarithmic equations with multiple logarithms

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Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

5 x^{2}+15 x-140=0

\newline

lesser

x=

\newline

greater

x=

Factor Quadratic Equation: First, we need to factor the quadratic equation $5x^2 + 15x - 140 = 0$ . We look for two numbers that multiply to $5*(-140) = -700$ and add up to $15$ . The numbers that satisfy these conditions are $35$ and $-20$ . So we can rewrite the equation as $5x^2 + 35x - 20x - 140 = 0$ .
Factor by Grouping: Next, we factor by grouping. $\newline$ We group the terms as follows: $(5x^2 + 35x) - (20x + 140) = 0$ . $\newline$ Then we factor out the common factors in each group: $5x(x + 7) - 20(x + 7) = 0$ .
Factor Common Binomial: Now we can factor out the common binomial factor $(x + 7)$ : $(5x - 20)(x + 7) = 0.$
Apply Zero Product Property: We now have the product of two factors equal to zero. $\newline$ According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. $\newline$ So we set each factor equal to zero: $5x - 20 = 0$ and $x + 7 = 0$ .
Solve for x: Solving the first equation $5x - 20 = 0$ for $x$ gives us: $\newline$ $5x = 20$ $\newline$ $x = \frac{20}{5}$ $\newline$ $x = 4$ .
Final Solutions: Solving the second equation $x + 7 = 0$ for $x$ gives us: $x = -7$ .
Final Solutions: Solving the second equation $x + 7 = 0$ for $x$ gives us: $x = -7$ .We have found two solutions: $x = 4$ and $x = -7$ . To answer the question prompt, we order them from least to greatest: lesser $x = -7$ greater $x = 4$ .