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Simplifying
x(x + 7) = (2x + -1)(x + 4)
Reorder the terms:
x(7 + x) = (2x + -1)(x + 4)
(7 * x + x * x) = (2x + -1)(x + 4)
(7x + x2) = (2x + -1)(x + 4)
Reorder the terms:
7x + x2 = (-1 + 2x)(x + 4)
Reorder the terms:
7x + x2 = (-1 + 2x)(4 + x)
Multiply (-1 + 2x) * (4 + x)
7x + x2 = (-1(4 + x) + 2x * (4 + x))
7x + x2 = ((4 * -1 + x * -1) + 2x * (4 + x))
7x + x2 = ((-4 + -1x) + 2x * (4 + x))
7x + x2 = (-4 + -1x + (4 * 2x + x * 2x))
7x + x2 = (-4 + -1x + (8x + 2x2))
Combine like terms: -1x + 8x = 7x
7x + x2 = (-4 + 7x + 2x2)
Add '-7x' to each side of the equation.
7x + -7x + x2 = -4 + 7x + -7x + 2x2
Combine like terms: 7x + -7x = 0
0 + x2 = -4 + 7x + -7x + 2x2
x2 = -4 + 7x + -7x + 2x2
Combine like terms: 7x + -7x = 0
x2 = -4 + 0 + 2x2
x2 = -4 + 2x2
Solving
x2 = -4 + 2x2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x2' to each side of the equation.
x2 + -2x2 = -4 + 2x2 + -2x2
Combine like terms: x2 + -2x2 = -1x2
-1x2 = -4 + 2x2 + -2x2
Combine like terms: 2x2 + -2x2 = 0
-1x2 = -4 + 0
-1x2 = -4
Divide each side by '-1'.
x2 = 4
Simplifying
x2 = 4
Take the square root of each side:
x = {-2, 2}
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