1 - x^2 - (3x+1)/2 = -(x^2)/4 + 5x - (3x^2)/4

asked by guest
on Apr 04, 2025 at 6:44 pm



You asked:

Solve the equation 1−x2−3x+12=−x24+5x−3x241 - {x}^{2} - \frac{3 x + 1}{2} = \frac{-{x}^{2}}{4} + 5 x - \frac{3 {x}^{2}}{4} for the variable xx.

MathBot Answer:

The solution is: x=113=0.0769230‾x = \frac{1}{13} = 0.0\overline{769230}

1−x2−3x+12=−x24+5x−3x24−x2−3x2+12=−x2+5x−13x2=−12x=113\begin{aligned}1 - {x}^{2} - \frac{3 x + 1}{2} &= \frac{-{x}^{2}}{4} + 5 x - \frac{3 {x}^{2}}{4}\\- x^{2} - \frac{3 x}{2} + \frac{1}{2} &= - x^{2} + 5 x\\- \frac{13 x}{2} &= - \frac{1}{2}\\x &= \frac{1}{13}\end{aligned}

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