The exact solutions of x² + 7x - 4 = 0 are x = -7 + √65/2 and x = -7 - √65/2.
What is the root of the quadratic equation?
The values of variables satisfying the given quadratic equation are called their roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0. The real roots of equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersects the x-axis.
x² = 4 -7x
Need to rewrite the equation in quadratic form.
Add 7x to each side:
x² +7x = 4
Subtract 4 from each side:
x² + 7x - 4 = 0
Now using the quadratic formula -b +/-√(b^2-4(ac)) / 2a
We can solve for x.
a = 1, b = 7 and c = -4
Put the values in the formula:
-7 +/- √(7^2 -4(1-4)) / 2*1
-7 +/- √65 /2
The exact answers are:
x = -7 + √65 / 2 and x = -7 - √65 / 2
Hence, the exact solutions of x² + 7x - 4 = 0 are x = -7 + √65/2 and x = -7 - √65/2.
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