Substituting gives \( x^2 + 2x - 15 = 0 \).

["SEO Article: Solving the Quadratic Equation ( x^2 + 2x - 15 = 0 ) – Step-by-Step Guide", "Solving quadratic equations is a fundamental skill in algebra, and understanding how to substitute and solve ( x^2 + 2x - 15 = 0 ) can help students and learners master essential problem-solving techniques. This article walks through the process of substituting and solving the equation step by step, explaining key methods such as factoring, completing the square, and using the quadratic formula. Whether you're reviewing for school or building math fluency, mastering this equation is a crucial step in algebraic proficiency.", "---", "### Why Solve ( x^2 + 2x - 15 = 0 )?", "The equation ( x^2 + 2x - 15 = 0 ) is a standard quadratic equation in the form ( ax^2 + bx + c = 0 ), where ( a = 1 ), ( b = 2 ), and ( c = -15 ). Solving such equations develops critical thinking, helps understand parabolas and their intersections with the x-axis, and strengthens algebraic manipulation skills.", "---", "### Step-by-Step Substitution and Solution", "#### Method 1: Factoring – The Most Common Approach\nSince ( a = 1 ), we look for two numbers that multiply to ( c = -15 ) and add to ( b = 2 ).\nNumbers: ( 5 ) and ( -3 ) (because ( 5 \ imes (-3) = -15 ) and ( 5 + (-3) = 2 )).", "Substituting into factored form:\n[\n(x + 5)(x - 3) = 0\n]", "By the zero-product property:\n- ( x + 5 = 0 ) → ( x = -5 )\n- ( x - 3 = 0 ) → ( x = 3 )", "✅ Solutions: ( x = -5 ) or ( x = 3 )", "---", "#### Method 2: Using the Quadratic Formula\nFor equations that don’t factor easily, the quadratic formula\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]\nis invaluable.", "With ( a = 1 ), ( b = 2 ), ( c = -15 ):\n[\nx = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-15)}}{2(1)} = \frac{-2 \pm \sqrt{4 + 60}}{2} = \frac{-2 \pm \sqrt{64}}{2}\n]\n[\nx = \frac{-2 \pm 8}{2}\n]", "Calculating both solutions:\n- ( x = \frac{-2 + 8}{2} = \frac{6}{2} = 3 )\n- ( x = \frac{-2 - 8}{2} = \frac{-10}{2} = -5 )", "✅ Same solutions confirmed: ( x = 3 ) or ( x = -5 )", "---", "#### Method 3: Completing the Square\nRewriting the equation:\n[\nx^2 + 2x = 15\n]\nAdd ( (b/2)^2 = (2/2)^2 = 1 ) to both sides:\n[\nx^2 + 2x + 1 = 15 + 1 \quad \Rightarrow \quad (x + 1)^2 = 16\n]", "Take square roots:\n[\nx + 1 = \pm 4\n]\n[\nx = -1 \pm 4\n]", "Solutions:\n- ( x = -1 + 4 = 3 )\n- ( x = -1 - 4 = -5 )", "✅ Final answers again: ( x = 3 ), ( x = -5 )", "---", "### Tips for Substituting in Any Quadratic Equation ( ax^2 + bx + c = 0 )", "- Identify coefficients ( a ), ( b ), and ( c ) quickly.\n- Consider factoring first—often the fastest method.\n- Use the quadratic formula when factoring is difficult.\n- Completing the square is useful for understanding vertex form and graphing.\n- After substitution, always simplify fully before solving.", "---", "### Real-World Applications", "Quadratic equations model real-life scenarios such as projectile motion, profit optimization, and area calculations. Understanding how to substitute and solve equations like ( x^2 + 2x - 15 = 0 ) prepares students for advanced math, science, and engineering applications.", "---", "### Summary", "The equation ( x^2 + 2x - 15 = 0 ) serves as a core example of solving quadratic equations through substitution and factoring. Using multiple methods—factoring, quadratic formula, completing the square—reinforces conceptual understanding and problem-solving flexibility. Mastering this equation strengthens algebra foundations essential for higher-level math.", "---", "Keywords (SEO Optimization):\nquadratic equation solutions, solve ( x^2 + 2x - 15 = 0 ), factoring quadratic, quadratic formula steps, completing the square, algebra tutorial, solving quadratics, substitution method, algebraic equations.", "Meta Description:\nLearn how to substitute and solve ( x^2 + 2x - 15 = 0 ) using factoring, the quadratic formula, and completing the square. Step-by-step solutions and real-world applications included.", "---", "Start mastering quadratic equations today—substitute, solve, and unlock deeper algebraic mastery!"]