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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 x . Enter the solutions from least to greatest.\newline5x2+15x−140=0 5 x^{2}+15 x-140=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline5x2+15x−140=0 5 x^{2}+15 x-140=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Factor Quadratic Equation: Factor the quadratic equation.\newlineTo solve the quadratic equation 5x2+15x−140=05x^2 + 15x - 140 = 0, we look for factors of 5x25x^2 that add up to 15x15x and multiply to give −140×5=−700-140 \times 5 = -700.\newlineWe can factor the quadratic as follows:\newline5x2+35x−20x−140=05x^2 + 35x - 20x - 140 = 0\newlineGrouping the terms, we get:\newline(5x2+35x)−(20x+140)=0(5x^2 + 35x) - (20x + 140) = 0\newline5x(x+7)−20(x+7)=05x(x + 7) - 20(x + 7) = 0\newlineNow, we can factor out (x+7)(x + 7):\newline(5x−20)(x+7)=0(5x - 20)(x + 7) = 0
  2. Solve for x: Solve for x.\newlineWe have two factors set to zero, which gives us two possible solutions for xx:\newline5x−20=05x - 20 = 0 or x+7=0x + 7 = 0\newlineSolving the first equation for xx gives us:\newline5x=205x = 20\newlinex=205x = \frac{20}{5}\newlinex=4x = 4\newlineSolving the second equation for xx gives us:\newlinex=−7x = -7
  3. Identify Values of xx: Identify the lesser and greater values of xx. Comparing the two solutions, x=4x = 4 and x=−7x = -7, we can see that −7-7 is the lesser value and 44 is the greater value.

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