Then, \(x = rac{8 \pm \sqrt{16}}{4} = rac{8 \pm 4}{4}\).

["Understanding the Expression: (x = \frac{8 \pm \sqrt{16}}{4} = \frac{8 \pm 4}{4}) – A Step-by-Step Breakdown", "When tackling quadratic equations, one of the most essential tools is the quadratic formula, which provides a reliable method for finding solutions of any equation in the standard form:", "[\nax^2 + bx + c = 0\n]", "In this article, we’ll explore a classic application of the quadratic formula using the example:", "[\nx = \frac{8 \pm \sqrt{16}}{4} = \frac{8 \pm 4}{4}\n]", "### What Does the Expression Mean?", "The equation (x = \frac{8 \pm \sqrt{16}}{4}) arises from substituting values into the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Here:\n- (a = 1),\n- (b = 8),\n- (c = 0)", "So, the discriminant ( \sqrt{b^2 - 4ac} = \sqrt{8^2 - 4(1)(0)} = \sqrt{64} = 8 ). However, ( \sqrt{16} ) mentioned in the expression is actually ( \sqrt{16} = 4 ), which suggests a slight simplification or typographical shorthand — possibly aligning with a related but different equation or simplification path. But we’ll proceed with the correct interpretation.", "### Simplifying the Expression\nSince ( \sqrt{16} = 4 ), we rewrite the formula:", "[\nx = \frac{8 \pm 4}{4}\n]", "This signifies two possible solutions:", "[\nx = \frac{8 + 4}{4} = \frac{12}{4} = 3\n]\nand\n[\nx = \frac{8 - 4}{4} = \frac{4}{4} = 1\n]", "Thus, the equation (x = \frac{8 \pm \sqrt{16}}{4}) simplifies cleanly to (x = 3) and (x = 1), the two real roots of the quadratic equation.", "### Solving the Original Equation\nTo confirm, let’s derive the corresponding quadratic equation. Starting from:", "[\nx = \frac{8 \pm 4}{4}\n]", "Multiply both sides by 4:", "[\n4x = 8 \pm 4\n]", "This gives two equations:", "1. (4x = 8 + 4 = 12 \Rightarrow x = 3)\n2. (4x = 8 - 4 = 4 \Rightarrow x = 1)", "Replacing (x) in (ax^2 + bx + c = 0) gives:", "[\n(4)(x)^2 + (-4)(x) + 0 = 0 \Rightarrow 4x^2 - 4x = 0\n]", "Factoring:", "[\n4x(x - 1) = 0 \Rightarrow x = 0 \quad \ ext{or} \quad x = 1\n]", "Wait! Note the discrepancy: our initial roots (x = 1) and (x = 3) seem inconsistent with (4x^2 - 4x = 0). Let’s recheck values.", "Actually, using ( \sqrt{16} = 4 ), from:", "[\nx = \frac{8 \pm \sqrt{16}}{4} = \frac{8 \pm 4}{4}\n]", "we get:", "[\nx = \frac{12}{4} = 3 \quad \ ext{and} \quad x = \frac{4}{4} = 1\n]", "Plug (x = 1) and (x = 3) back into (4x^2 - 4x = 0):", "- For (x = 1): (4(1)^2 - 4(1) = 0)\n- For (x = 3): (4(3)^2 - 4(3) = 36 - 12 = 24 <br/>\neq 0)", "Correction:\nThere’s an inconsistency — only (x = 1) satisfies the simplified quadratic. Therefore, the original expression might assume a different equation or includes an error.", "But assuming intended values produce (x = 1) and (x = 3), rewrite correctly:", "Use proper discriminant: ( \sqrt{b^2 - 4ac} = \sqrt{64} = 8 )", "So correct form is:", "[\nx = \frac{-8 \pm 8}{4}\n]", "But if using ( \pm \sqrt{16} = \pm 4 ) over (4), only extreme roots (x = 1) and (x = 3) emerge — suggesting need for consistent parameters.", "Key Takeaway:\nWhen evaluating (x = \frac{8 \pm \sqrt{16}}{4}), the correct results are:", "[\nx = \frac{8 + 4}{4} = 3, \quad x = \frac{8 - 4}{4} = 1\n]", "These values correspond to roots of the equation (4x^2 - 4x = 0) only if the original quadratic was adjusted accordingly. Otherwise, confirm equation coefficients.", "### Why This Expression Matters\nUnderstanding how to expand and interpret such expressions builds foundational algebra skills crucial for:", "- Solving quadratic equations efficiently\n- Analyzing graphs and roots of polynomials\n- Applying math in physics, engineering, and finance", "### Final Thoughts\nWhile (x = \frac{8 \pm \sqrt{16}}{4}) simplifies to two distinct values, (x = 1) and (x = 3), the correct usage depends on matching the discriminant ( \sqrt{b^2 - 4ac} ). Ensuring accurate coefficients prevents errors — but mastering these transformations strengthens your algebraic toolkit.", "Keywords: quadratic formula, solving quadratics, (x = \frac{8 \pm \sqrt{16}}{4}), roots of equations, algebra tutorial, discriminant calculation, mathematical expressions, solving equations step-by-step.", "---\nOptimize your math practice with clear, accurate expression simplification — your key to confident problem-solving!"]