En réarrangeant : \( 2x^2 + 2x - 84 = 0 \).

["# Rearranging Quadratic Equations: Solving ( 2x^2 + 2x - 84 = 0 )", "Solving quadratic equations is a fundamental skill in algebra, and rearranging equations in standard form is a key step for easier solving. In this article, we will walk through the process of rearranging and solving the quadratic equation:", "[\n2x^2 + 2x - 84 = 0\n]", "## Why Rearranging Helps", "The standard form of a quadratic equation is:", "[\nax^2 + bx + c = 0\n]", "Rearranging helps simplify the expression, make it easier to factor, apply the quadratic formula, or complete the square — all essential techniques for solving quadratics.", "## Step-by-Step: Rearranging and Solving ( 2x^2 + 2x - 84 = 0 )", "### 1. Start with the original equation:", "[\n2x^2 + 2x - 84 = 0\n]", "### 2. Rearrange into standard form (if needed)", "Although the equation is already in standard form, rearranging ensures clarity:", "[\n2x^2 + 2x = 84\n]", "### 3. Simplify (optional)", "Divide every term by 2 to simplify the equation:", "[\nx^2 + x = 42\n]", "### 4. Rearrange to set equal to zero", "Move 42 to the left side:", "[\nx^2 + x - 42 = 0\n]", "Now the equation is fully rearranged into standard quadratic form.", "---", "## Solving the Rearranged Equation", "### Step: Apply the quadratic formula", "The standard form ( x^2 + x - 42 = 0 ) gives:", "- ( a = 1 )\n- ( b = 1 )\n- ( c = -42 )", "The quadratic formula is:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Substitute the values:", "[\nx = \frac{-(1) \pm \sqrt{(1)^2 - 4(1)(-42)}}{2(1)}\n]", "[\nx = \frac{-1 \pm \sqrt{1 + 168}}{2}\n]", "[\nx = \frac{-1 \pm \sqrt{169}}{2}\n]", "[\nx = \frac{-1 \pm 13}{2}\n]", "### Two solutions emerge:", "[\nx = \frac{-1 + 13}{2} = \frac{12}{2} = 6\n]", "[\nx = \frac{-1 - 13}{2} = \frac{-14}{2} = -7\n]", "---", "## Verifying the Solutions", "Plug ( x = 6 ) back into the original equation:", "[\n2(6)^2 + 2(6) - 84 = 72 + 12 - 84 = 0 \quad \ ext{✔}\n]", "Plug ( x = -7 ):", "[\n2(-7)^2 + 2(-7) - 84 = 98 - 14 - 84 = 0 \quad \ ext{✔}\n]", "Both values satisfy the equation.", "---", "## Conclusion", "Rearranging quadratic expressions into standard form ( ax^2 + bx + c = 0 ) simplifies solving and improves clarity. For the equation\n[\n2x^2 + 2x - 84 = 0,\n]\nafter dividing by 2 to get ( x^2 + x - 42 = 0 ), applying the quadratic formula yields the solutions:", "[\nx = 6 \quad \ ext{and} \quad x = -7\n]", "Mastering rearrangement is key to efficiently solving quadratic equations in algebra.", "---", "### SEO Keywords:\n- rearranging quadratic equations\n- solving ( 2x^2 + 2x - 84 = 0 )\n- step-by-step quadratic formula\n- standard form of quadratic equations\n- quadratic solutions algebra\n- solving ( ax^2 + bx + c = 0 )", "---", "Optimize your understanding and practice by rearranging equations like ( 2x^2 + 2x - 84 = 0 ) step by step—this builds a strong foundation for advanced algebra."]