10-3x-x²=0

<p>To solve the equation 10-3x-x²=0, we can rearrange it to the form of a quadratic equation: -x² - 3x + 10 = 0.</p><p>To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:</p><p>The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:</p><p>x = (-b ± √(b² - 4ac)) / 2a</p><p>In our equation, a = -1, b = -3, and c = 10. Plugging these values into the quadratic formula, we get:</p><p>x = (-(-3) ± √((-3)² - 4(-1)(10))) / (2(-1)) = (3 ± √(9 + 40)) / (-2) = (3 ± √49) / (-2) = (3 ± 7) / (-2)</p><p>So, the two solutions for x are:</p><p>x₁ = (3 + 7) / (-2) = 10 / (-2) = -5 x₂ = (3 - 7) / (-2) = -4 / (-2) = 2</p><p>Therefore, the equation 10-3x-x²=0 has two solutions: x = -5 and x = 2.</p>