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3x + 1/4x2 = 64. Find x

June 12, 2026Mathematics

ScanSolve AI Answer

Answer

\frac{-3 \pm \sqrt{265}}{2}

5 steps

Write the given equation.
The equation from the image is:
$3x + x^2 = 64$
Rearrange the equation into standard quadratic form $ax^2 + bx + c = 0$ .
Subtract 64 from both sides and reorder the terms:
$x^2 + 3x - 64 = 0$
Identify the coefficients $a, b, c$.
For the equation $x^2 + 3x - 64 = 0$ :
$a = 1$
$b = 3$
$c = -64$
Apply the quadratic formula.
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute the values of $a, b, c$ :
$x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-64)}}{2(1)}$
Simplify the expression.
Calculate the terms inside the square root:
$x = \frac{-3 \pm \sqrt{9 + 256}}{2}$ $x = \frac{-3 \pm \sqrt{265}}{2}$
The two possible values for $x$ are:
$x_1 = \frac{-3 + \sqrt{265}}{2}$ $x_2 = \frac{-3 - \sqrt{265}}{2}$
The exact values for $x$ are $\boxed{\frac{-3 \pm \sqrt{265}}{2}}$ .