1.2.2 Hence solve for \( x \) correct to TWO decimal places: \( x(3 x+13)=11 \) \( 1.23 \quad \sqrt{x-3}-4-5 \) 1.2.4. Solve for \( <\sqrt{(x-2)^{-3}}=64 \) 1.3 1.3.1 Factorisc: \( y^{2}-9 x^{2} \)

Solve the equation \( x(3x+13)=11 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x\left(3x+13\right)=11\) - step1: Expand the expression: \(3x^{2}+13x=11\) - step2: Move the expression to the left side: \(3x^{2}+13x-11=0\) - step3: Solve using the quadratic formula: \(x=\frac{-13\pm \sqrt{13^{2}-4\times 3\left(-11\right)}}{2\times 3}\) - step4: Simplify the expression: \(x=\frac{-13\pm \sqrt{13^{2}-4\times 3\left(-11\right)}}{6}\) - step5: Simplify the expression: \(x=\frac{-13\pm \sqrt{301}}{6}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{-13+\sqrt{301}}{6}\\&x=\frac{-13-\sqrt{301}}{6}\end{align}\) - step7: Rewrite the fraction: \(\begin{align}&x=\frac{-13+\sqrt{301}}{6}\\&x=-\frac{13+\sqrt{301}}{6}\end{align}\) - step8: Rewrite: \(x_{1}=-\frac{13+\sqrt{301}}{6},x_{2}=\frac{-13+\sqrt{301}}{6}\) The equation provided is not in a format that can be solved directly. If you could provide the equation in a standard format, I would be happy to assist you further.

Unable to solve the equation.

Solve the equation \( \sqrt{(x-2)^{-3}}=64 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\sqrt{\left(x-2\right)^{-3}}=64\) - step1: Find the domain: \(\sqrt{\left(x-2\right)^{-3}}=64,x>2\) - step2: Simplify the root: \(\frac{1}{\sqrt{\left(x-2\right)^{3}}}=64\) - step3: Cross multiply: \(1=\sqrt{\left(x-2\right)^{3}}\times 64\) - step4: Simplify the equation: \(1=64\sqrt{\left(x-2\right)^{3}}\) - step5: Swap the sides: \(64\sqrt{\left(x-2\right)^{3}}=1\) - step6: Divide both sides: \(\frac{64\sqrt{\left(x-2\right)^{3}}}{64}=\frac{1}{64}\) - step7: Divide the numbers: \(\sqrt{\left(x-2\right)^{3}}=\frac{1}{64}\) - step8: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{\left(x-2\right)^{3}}\right)^{2}=\left(\frac{1}{64}\right)^{2}\) - step9: Evaluate the power: \(\left(x-2\right)^{3}=\frac{1}{4096}\) - step10: Simplify the equation: \(\sqrt[3]{\left(x-2\right)^{3}}=\sqrt[3]{\frac{1}{4096}}\) - step11: Calculate: \(x-2=\sqrt[3]{\frac{1}{4096}}\) - step12: Simplify the root: \(x-2=\frac{1}{16}\) - step13: Move the constant to the right side: \(x=\frac{1}{16}+2\) - step14: Add the numbers: \(x=\frac{33}{16}\) - step15: Check if the solution is in the defined range: \(x=\frac{33}{16},x>2\) - step16: Find the intersection: \(x=\frac{33}{16}\) - step17: Check the solution: \(x=\frac{33}{16}\) The solution to the equation \( \sqrt{(x-2)^{-3}}=64 \) is \( x = \frac{33}{16} \) or \( x = 2.0625 \).

\( x = \frac{33}{16} \) or \( x = 2.0625 \)

Factor the expression \( y^{2}-9x^{2} \). Factor the expression by following steps: - step0: Factor: \(y^{2}-9x^{2}\) - step1: Rewrite the expression: \(y^{2}-\left(3x\right)^{2}\) - step2: Factor the expression: \(\left(y-3x\right)\left(y+3x\right)\) The factored form of the expression \( y^{2}-9x^{2} \) is \( (y-3x)(y+3x) \).