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Solve for 
x. Enter the solutions from least to greatest.
Round to two decimal places.

(x+15)^(2)-10=0
lesser 
x=
greater 
x=

Solve for x x . Enter the solutions from least to greatest.\newlineRound to two decimal places.\newline(x+15)210=0 (x+15)^{2}-10=0 \newlinelesser x= x= \newlinegreater x= x=

Full solution

Q. Solve for x x . Enter the solutions from least to greatest.\newlineRound to two decimal places.\newline(x+15)210=0 (x+15)^{2}-10=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Write and prepare equation: Write down the given equation and prepare to solve for xx.\newlineGiven equation: (x+15)210=0(x+15)^{2}-10=0\newlineWe need to solve for xx by isolating the term with xx on one side of the equation.
  2. Isolate squared term: Add 1010 to both sides of the equation to isolate the squared term.\newline(x+15)210+10=0+10(x+15)^{2}-10+10=0+10\newline(x+15)2=10(x+15)^{2}=10
  3. Take square root: Take the square root of both sides of the equation to solve for x+15x+15.(x+15)2=±10\sqrt{(x+15)^{2}}=\pm\sqrt{10}x+15=±10x+15=\pm\sqrt{10}
  4. Subtract 1515: Subtract 1515 from both sides of the equation to solve for xx.\newlinex+1515=±1015x+15-15=\pm\sqrt{10}-15\newlinex=±1015x=\pm\sqrt{10}-15
  5. Calculate numerical values: Calculate the numerical values of xx, rounding to two decimal places.\newlinex=10153.161511.84x = \sqrt{10} - 15 \approx 3.16 - 15 \approx -11.84 (lesser value)\newlinex=10153.161518.16x = -\sqrt{10} - 15 \approx -3.16 - 15 \approx -18.16 (greater value)\newlineNote: The "greater" and "lesser" labels seem to be reversed here, as 18.16-18.16 is less than 11.84-11.84. We will correct this in the final answer.

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