What is the solution to the equation x(x-1)=7

Given x(x-1) =7,

Expand:
x(x) - x(1) = 7

Simplify:
x^2 - x = 7

Subtract 7 from both sides of the equations:
x^2 - x - 7 = 0

Use the quadratic formula,
a = 1, b = -1, c = -7

Solution 1:
x = [-b + sqrt(b^2 - 4ac)]/2a
= [-(-1) + sqrt((-1)^2 - 4(1)(-7))]/2(1)
= [1 + sqrt(29]/2
= 3.19 (to 3 significant figures)

Solution 2:
x = [-b - sqrt(b^2 - 4ac)]/2a
= [-(-1) - sqrt((-1)^2 - 4(1)(-7))]/2(1)
= [1 - sqrt(29]/2
= -2.19 (to 3 significant figures)

Nur has your right answer: [1±√29] /2, but where you might be
confused is this line: x² - (1/2)² = 7 + (1/2)² Which should be
x² -x +(1/2)² = 7 + (1/2)².

She is solving by completing the square; my general preferences are
factoring first (because it's usually faster, if feasible); otherwise use
the quadratic formula: x =[-b ±√(b² -4ac)] /(2a) where your quadratic is
of the form ax² +bx +c =0

[Your quadratic would look this way: x² -x -7 = 0.]

x^2-x=7

x^2-x-7=0

You can't factor, because there are no factors of -7 that add up to -1. So use the quadratic formula:
-(-1) ± √ (-1)^2 -4(1)(-7) /2(1)

1 ±√29 /2

That can be your final answer. If you want to be specific, the square root of 29 is approximately 5.385, so you'll have 6.385/2 and -4.385/2 as your two answers.

x(x-1)=7
x^2 - x = 7
x^2 - x - 7 = 0


Solution here:
http://www.quickmath.com/webMathematica3…

x(x-1) = 7
x^2 -x = 7
x^2 -x -7 =0

use the quadratic formula

(1 + or - the square root of (1 + 28)) over 2

(1 + or - the square root of 29) over 2

x(x-1)=7
x² - x = 7
x² - (1/2)² = 7 + (1/2)²
(x – ½)² = 29/4
x – ½ = ±√(29/4)
x = ½ ± ½√29
x = ½(1 ± √29)

x = ½(1 + √29)
or
x = ½(1 - √29)

x^2-x-7=0
(x-1/2)^2-29/4=0
(x-1/2)^2={sqrt(29/4)}^2
x=1/2+1/2sqrt(29) or
x=1/2-1/2sqrt(29)

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