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Solve for x. Enter the solutions from least to greatest. 5x^(2)+3=83 lesser x= greater x=

Solve for x x .\newlineEnter the solutions from least to greatest.\newline5x2+3=83 5 x^{2}+3=83 \newlinelesser x= x= \newlinegreater x= x=

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Full solution

Q. Solve for x x .\newlineEnter the solutions from least to greatest.\newline5x2+3=83 5 x^{2}+3=83 \newlinelesser x= x= \newlinegreater x= x=
  1. Isolate x term: First, we need to isolate the term with the variable xx on one side of the equation. We start by subtracting 33 from both sides of the equation to get rid of the constant term on the left side.\newline5x2+3=835x^2 + 3 = 83\newline5x2=83−35x^2 = 83 - 3\newline5x2=805x^2 = 80
  2. Divide by 55: Next, we divide both sides of the equation by 55 to solve for x2x^2.\newline5x25=805\frac{5x^2}{5} = \frac{80}{5}\newlinex2=16x^2 = 16
  3. Take square root: Now, we take the square root of both sides to solve for x. Remember that taking the square root of a number yields two solutions: one positive and one negative.\newlinex2=±16\sqrt{x^2} = \pm\sqrt{16}\newlinex=±4x = \pm4
  4. List solutions: We have two solutions for x: x=4x = 4 and x=−4x = -4. We need to list them from least to greatest.\newlinelesser x=−4x = -4\newlinegreater x=4x = 4

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