Isolve the following equation: x^2+5=4x For multiple solutions separate your answers by a comma. square

We are tasked with solving the quadratic equation:<br /><br />\[<br />x^2 + 5 = 4x<br />\]<br /><br />### Step 1: Rearrange the equation into standard quadratic form<br />The standard form of a quadratic equation is:<br /><br />\[<br />ax^2 + bx + c = 0<br />\]<br /><br />Rearranging \(x^2 + 5 = 4x\), we subtract \(4x\) from both sides:<br /><br />\[<br />x^2 - 4x + 5 = 0<br />\]<br /><br />### Step 2: Solve using the quadratic formula<br />The quadratic formula is given by:<br /><br />\[<br />x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}<br />\]<br /><br />Here, \(a = 1\), \(b = -4\), and \(c = 5\). Substituting these values into the formula:<br /><br />\[<br />x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(5)}}{2(1)}<br />\]<br /><br />Simplify step-by-step:<br /><br />1. Calculate \(-b\):<br /> \[<br /> -(-4) = 4<br /> \]<br /><br />2. Compute the discriminant (\(b^2 - 4ac\)):<br /> \[<br /> (-4)^2 - 4(1)(5) = 16 - 20 = -4<br /> \]<br /><br />3. Substitute into the formula:<br /> \[<br /> x = \frac{4 \pm \sqrt{-4}}{2}<br /> \]<br /><br />### Step 3: Simplify the square root of the negative discriminant<br />Since the discriminant is negative (\(-4\)), the solutions will involve imaginary numbers. Recall that \(\sqrt{-1} = i\), so:<br /><br />\[<br />\sqrt{-4} = 2i<br />\]<br /><br />Substitute this back into the equation:<br /><br />\[<br />x = \frac{4 \pm 2i}{2}<br />\]<br /><br />### Step 4: Simplify the expression<br />Split the terms in the numerator:<br /><br />\[<br />x = \frac{4}{2} \pm \frac{2i}{2}<br />\]<br /><br />Simplify each term:<br /><br />\[<br />x = 2 \pm i<br />\]<br /><br />### Final Answer:<br />The solutions to the equation are:<br /><br />\[<br />\boxed{2 + i, 2 - i}<br />\]