Rewrite: \( x(x - 3) = 2^2 = 4 \).

["# Rewrite and Solve: A Step-by-Step Guide to Solving ( x(x - 3) = 4 )", "Solving equations is one of the fundamental skills in algebra, yet many learners struggle with rewriting expressions and applying algebraic identities. One common problem is rewriting and solving ( x(x - 3) = 4 ), a quadratic equation often simplified using expansion and factorization. In this article, we’ll explore how to effectively rewrite the equation, solve it step-by-step, and understand the mathematical principles behind the solution—all optimized for SEO to help students, educators, and math enthusiasts improve their algebraic skills.", "## Understanding the Equation: ( x(x - 3) = 4 )", "The equation ( x(x - 3) = 4 ) represents a quadratic expression. At first glance, comparing both sides directly may cause confusion. The left-hand side is a product, while the right-hand side is a constant. A powerful first step is rewriting the equation in standard quadratic form, which improves clarity and eases the solving process. This aligns with best practices in algebra education and search optimization.", "### Step 1: Expand and Rewrite in Standard Form", "Expand the left-hand side:", "[\nx(x - 3) = x^2 - 3x\n]", "Now substitute back into the equation:", "[\nx^2 - 3x = 4\n]", "Bring all terms to one side to form a standard quadratic:", "[\nx^2 - 3x - 4 = 0\n]", "This step is crucial—writing the expression in standard form ( ax^2 + bx + c = 0 )—and is frequently searched terms like "how to rewrite ( x(x-3)=4 ) to standard form".", "### Step 2: Factor the Quadratic Equation", "Now solve ( x^2 - 3x - 4 = 0 ). We look for two numbers that multiply to ( -4 ) (product of ( a \cdot c )) and add to ( -3 ) (coefficient of ( x )).", "Those numbers are ( -4 ) and ( +1 ):", "[\n(x - 4)(x + 1) = 0\n]", "This factored form makes it easy to apply the zero-product property: if a product equals zero, then one of the factors must be zero.", "### Step 3: Solve for ( x )", "Set each factor equal to zero:", "[\nx - 4 = 0 \quad \Rightarrow \quad x = 4\n]\n[\nx + 1 = 0 \quad \Rightarrow \quad x = -1\n]", "Thus, the solutions are ( x = 4 ) and ( x = -1 ).", "### Step 4: Verify Solutions In both Original Equation", "Always substitute each solution back into the original equation to confirm validity:", "For ( x = 4 ):", "[\n4(4 - 3) = 4 \ imes 1 = 4 \quad \ ext{(✓)}\n]", "For ( x = -1 ):", "[\n-1(-1 - 3) = -1 \ imes (-4) = 4 \quad \ ext{(✓)}\n]", "Both solutions satisfy the equation—important for catching algebraic errors.", "## Alternative Approach: Using Algebraic Imputation of the Binomial Square", "When initially presented as ( x(x - 3) = 4 ), recognizing a near-standard identity helps streamline solution. Though not a direct square, creative rewriting supports deeper understanding.", "Observe:", "[\nx(x - 3) = 4 \quad \Rightarrow \quad x^2 - 3x = 4 \quad \ ext{(as before)}\n]", "Although not a perfect square, completing the square or substitution remains valid—showing how rewriting enables advanced manipulation.", "### Summary of Solved Equation", "Rewriting ( x(x - 3) = 4 ) leads through expansion and standard form to a solvable quadratic. Key takeaways:", "- Expand expressions to standard form: ( x^2 - 3x - 4 = 0 )\n- Factor: ( (x - 4)(x + 1) = 0 )\n- Solutions: ( x = 4 ) and ( x = -1 )\n- Verification ensures accuracy and builds problem-solving confidence", "## Why This Matters for Learning Algebra", "Mastering quadratic equations and expression manipulation strengthens analytical reasoning and foundational math fluency. This problem exemplifies how rewriting and standardizing algebraic forms transforms complex expressions into solvable forms—essential both for exams and real-world applications.", "For educators, this article provides a clear, keyword-rich example optimized for search engines, covering essential terms like "solve quadratic equation by rewriting", "algebraic steps for ( x(x-3)=4 )", and "how to factor ( x^2 - 3x - 4 = 0 )" to boost visibility and student engagement.", "---", "### Final Answer", "The solutions to ( x(x - 3) = 4 ) are ( \boxed{x = 4} ) and ( \boxed{x = -1} ). Rewriting the equation into standard quadratic form and applying factorization enables systematic solving, reinforcing key algebraic techniques valuable across academic and professional contexts."]