QuestionJuly 15, 2025

Solve for x. 4x^2+12x=-5 If there is more than one solution , separate them with commas. If there is no solution, click on "No solution." x= square

Solve for x. 4x^2+12x=-5 If there is more than one solution , separate them with commas. If there is no solution, click on "No solution." x= square
Solve for x. 4x^2+12x=-5 If there is more than one solution , separate them with commas. If there is no solution, click on "No solution." x= square

Solution
4.1(361 votes)

Answer

x = -\frac{1}{2}, -\frac{5}{2} Explanation 1. Move all terms to one side Rewrite the equation as 4x^2 + 12x + 5 = 0. 2. Use the quadratic formula The quadratic formula is **x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. Here, a = 4, b = 12, and c = 5. 3. Calculate the discriminant b^2 - 4ac = 12^2 - 4 \cdot 4 \cdot 5 = 144 - 80 = 64. 4. Solve for x using the quadratic formula x = \frac{-12 \pm \sqrt{64}}{8} = \frac{-12 \pm 8}{8}. 5. Find the solutions x_1 = \frac{-12 + 8}{8} = \frac{-4}{8} = -\frac{1}{2}; x_2 = \frac{-12 - 8}{8} = \frac{-20}{8} = -\frac{5}{2}.

Explanation

1. Move all terms to one side<br /> Rewrite the equation as $4x^2 + 12x + 5 = 0$.<br />2. Use the quadratic formula<br /> The quadratic formula is **$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**. Here, $a = 4$, $b = 12$, and $c = 5$.<br />3. Calculate the discriminant<br /> $b^2 - 4ac = 12^2 - 4 \cdot 4 \cdot 5 = 144 - 80 = 64$.<br />4. Solve for x using the quadratic formula<br /> $x = \frac{-12 \pm \sqrt{64}}{8} = \frac{-12 \pm 8}{8}$.<br />5. Find the solutions<br /> $x_1 = \frac{-12 + 8}{8} = \frac{-4}{8} = -\frac{1}{2}$; $x_2 = \frac{-12 - 8}{8} = \frac{-20}{8} = -\frac{5}{2}$.
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