Step-by-step explanation:
@.In general, given a{x}^{2}+bx+cax
2
+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
−4ac
)(x−
−b−
)
2 In this case, a=2a=2, b=24b=24 and c=35c=35.
2(x-\frac{-24+\sqrt{{24}^{2}-4\times 2\times 35}}{2\times 2})(x-\frac{-24-\sqrt{{24}^{2}-4\times 2\times 35}}{2\times 2})
2(x−
2×2
−24+
24
−4×2×35
−24−
3 Simplify.
2(x-\frac{-24+2\sqrt{74}}{4})(x-\frac{-24-2\sqrt{74}}{4})
4
−24+2
74
−24−2
4 Factor out the common term 22.
2(x-\frac{-2(12-\sqrt{74})}{4})(x-\frac{-24-2\sqrt{74}}{4})
−2(12−
5 Move the negative sign to the left.
2(x-(-\frac{2(12-\sqrt{74})}{4}))(x-\frac{-24-2\sqrt{74}}{4})
2(x−(−
2(12−
))(x−
6 Simplify \frac{2(12-\sqrt{74})}{4}
to \frac{12-\sqrt{74}}{2}
12−
.
2(x-(-\frac{12-\sqrt{74}}{2}))(x-\frac{-24-2\sqrt{74}}{4})
7 Remove parentheses.
2(x+\frac{12-\sqrt{74}}{2})(x-\frac{-24-2\sqrt{74}}{4})
2(x+
8 Factor out the common term 22.
2(x+\frac{12-\sqrt{74}}{2})(x-\frac{-2(12+\sqrt{74})}{4})
−2(12+
9 Move the negative sign to the left.
2(x+\frac{12-\sqrt{74}}{2})(x-(-\frac{2(12+\sqrt{74})}{4}))
)(x−(−
2(12+
))
10 Simplify \frac{2(12+\sqrt{74})}{4}
to \frac{12+\sqrt{74}}{2}
12+
2(x+\frac{12-\sqrt{74}}{2})(x-(-\frac{12+\sqrt{74}}{2}))
11 Remove parentheses.
2(x+\frac{12-\sqrt{74}}{2})(x+\frac{12+\sqrt{74}}{2})
)(x+
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Answers & Comments
Step-by-step explanation:
@.In general, given a{x}^{2}+bx+cax
2
+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 In this case, a=2a=2, b=24b=24 and c=35c=35.
2(x-\frac{-24+\sqrt{{24}^{2}-4\times 2\times 35}}{2\times 2})(x-\frac{-24-\sqrt{{24}^{2}-4\times 2\times 35}}{2\times 2})
2(x−
2×2
−24+
24
2
−4×2×35
)(x−
2×2
−24−
24
2
−4×2×35
)
3 Simplify.
2(x-\frac{-24+2\sqrt{74}}{4})(x-\frac{-24-2\sqrt{74}}{4})
2(x−
4
−24+2
74
)(x−
4
−24−2
74
)
4 Factor out the common term 22.
2(x-\frac{-2(12-\sqrt{74})}{4})(x-\frac{-24-2\sqrt{74}}{4})
2(x−
4
−2(12−
74
)
)(x−
4
−24−2
74
)
5 Move the negative sign to the left.
2(x-(-\frac{2(12-\sqrt{74})}{4}))(x-\frac{-24-2\sqrt{74}}{4})
2(x−(−
4
2(12−
74
)
))(x−
4
−24−2
74
)
6 Simplify \frac{2(12-\sqrt{74})}{4}
4
2(12−
74
)
to \frac{12-\sqrt{74}}{2}
2
12−
74
.
2(x-(-\frac{12-\sqrt{74}}{2}))(x-\frac{-24-2\sqrt{74}}{4})
2(x−(−
2
12−
74
))(x−
4
−24−2
74
)
7 Remove parentheses.
2(x+\frac{12-\sqrt{74}}{2})(x-\frac{-24-2\sqrt{74}}{4})
2(x+
2
12−
74
)(x−
4
−24−2
74
)
8 Factor out the common term 22.
2(x+\frac{12-\sqrt{74}}{2})(x-\frac{-2(12+\sqrt{74})}{4})
2(x+
2
12−
74
)(x−
4
−2(12+
74
)
)
9 Move the negative sign to the left.
2(x+\frac{12-\sqrt{74}}{2})(x-(-\frac{2(12+\sqrt{74})}{4}))
2(x+
2
12−
74
)(x−(−
4
2(12+
74
)
))
10 Simplify \frac{2(12+\sqrt{74})}{4}
4
2(12+
74
)
to \frac{12+\sqrt{74}}{2}
2
12+
74
.
2(x+\frac{12-\sqrt{74}}{2})(x-(-\frac{12+\sqrt{74}}{2}))
2(x+
2
12−
74
)(x−(−
2
12+
74
))
11 Remove parentheses.
2(x+\frac{12-\sqrt{74}}{2})(x+\frac{12+\sqrt{74}}{2})
2(x+
2
12−
74
)(x+
2
12+
74
)