Solve for x. x-sqrt(2x^(2)-18)=-3

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Isolate square root term: First, isolate the square root term by adding sqrt(2x^2 - 18) to both sides of the equation. x - sqrt(2x^2 - 18) + sqrt(2x^2 - 18) = -3 + sqrt(2x^2 - 18) This simplifies to: x = -3 + sqrt(2x^2 - 18)Square both sides: Next, square both sides of the equation to eliminate the square root. (-3 + sqrt(2x^2 - 18))^2 = x^2 Expanding the left side, we get: (-3)^2 + 2(-3)sqrt(2x^2 - 18) + (sqrt(2x^2 - 18))^2 = x^2 9 - 6sqrt(2x^2 - 18) + 2x^2 - 18 = x^2Simplify equation: Simplify the equation by combining like terms and moving all terms to one side. 9 - 6sqrt(2x^2 - 18) + 2x^2 - 18 - x^2 = 0 2x^2 - x^2 - 6sqrt(2x^2 - 18) - 9 = 0 x^2 - 6sqrt(2x^2 - 18) - 9 = 0Isolate square root term again: Now, we have a new equation with a square root term. To isolate the square root term again, add 9 to both sides and then add 6sqrt(2x^2 - 18) to both sides. x^2 - 9 = 6sqrt(2x^2 - 18)Square both sides again: Square both sides of the equation again to eliminate the square root. (x^2 - 9)^2 = (6sqrt(2x^2 - 18))^2 Expanding the left side, we get: x^4 - 18x^2 + 81 = 36(2x^2 - 18) x^4 - 18x^2 + 81 = 72x^2 - 648Combine like terms: Combine like terms and move all terms to one side to form a quartic equation. x^4 - 18x^2 - 72x^2 + 81 + 648 = 0 x^4 - 90x^2 + 729 = 0Factor quartic equation: Factor the quartic equation. (x^2 - 81)(x^2 - 9) = 0 This gives us two factors: x^2 - 81 and x^2 - 9.Solve for x: Set each factor equal to zero and solve for x. x^2 - 81 = 0 and x^2 - 9 = 0 x^2 = 81 and x^2 = 9 x = ±9 and x = ±3Check solutions: Check each solution in the original equation to ensure it does not introduce any extraneous solutions. For x = 9: 9 - sqrt(2(9)^2 - 18) = -3 9 - sqrt(162 - 18) = -3 9 - sqrt(144) = -3 9 - 12 = -3 -3 = -3 (Valid solution)

Solve for $x$ . $\newline$ $x-\sqrt{2 x^{2}-18}=-3$

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Solve for xxx.\newlinex−2x2−18=−3 x-\sqrt{2 x^{2}-18}=-3 x−2x2−18​=−3

Solve for $x$ . $\newline$ $x-\sqrt{2 x^{2}-18}=-3$