$$ 1 \leftarrow \quad $$ Solve. $$ \quad-\sqrt{10 x}+1=-9 $$

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Solve the equation $$ -\sqrt{10x}+1=-9 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$-\sqrt{10x}+1=-9$$
- step1: Find the domain:
  $$-\sqrt{10x}+1=-9,x\geq 0$$
- step2: Move the constant to the right side:
  $$-\sqrt{10x}=-9-1$$
- step3: Subtract the numbers:
  $$-\sqrt{10x}=-10$$
- step4: Divide both sides:
  $$\sqrt{10x}=10$$
- step5: Raise both sides to the $$2$$-th power$$:$$
  $$\left(\sqrt{10x}\right)^{2}=10^{2}$$
- step6: Evaluate the power:
  $$10x=100$$
- step7: Divide both sides:
  $$\frac{10x}{10}=\frac{100}{10}$$
- step8: Divide the numbers:
  $$x=10$$
- step9: Check if the solution is in the defined range:
  $$x=10,x\geq 0$$
- step10: Find the intersection:
  $$x=10$$
- step11: Check the solution:
  $$x=10$$
The solution to the equation $$-\sqrt{10x}+1=-9$$ is $$x=10$$.
$$ x=10 $$

\( 1 \leftarrow \quad \) Solve. \( \quad-\sqrt{10 x}+1=-9 \)

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