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Solve the quadratic:
-x2+12x+540 = 575
The quadratic you entered is not in standard form:
ax2 + bx + c = 0
a = -1, b = 12, c = -35
x = | -b ± √b2 - 4ac |
2a |
-b = -(12)
-b = -12
Δ = b2 - 4ac:
Δ = 122 - 4 x -1 x -35
Δ = 144 - 140
Δ = 4 <--- Discriminant
Since Δ > 0, we expect two real roots.
√Δ = √(4)
√Δ = 2
Numerator 1 = -b + √Δ
Numerator 1 = -12 + 2
Numerator 1 = -10
Numerator 2 = -b - √Δ
Numerator 2 = -12 - 2
Numerator 2 = -14
Denominator = 2 * a
Denominator = 2 * -1
Denominator = -2
Solution 1 = | Numerator 1 |
Denominator |
Solution 1 = | -10 |
-2 |
Solution 1 = 5
Solution 2 = | Numerator 2 |
Denominator |
Solution 2 = | -14 |
-2 |
Solution 2 = 7
(Solution 1, Solution 2) = (5, 7)
(5)2 + 12(5) - 35 ? 0
(25) + 6035 ? 0
-25 + 6035 ? 0
0 = 0
(7)2 + 12(7) - 35 ? 0
(49) + 8435 ? 0
-49 + 8435 ? 0
0 = 0