Solve for x
x = -\frac{7}{2} = -3\frac{1}{2} = -3.5
x = -\frac{3}{2} = -1\frac{1}{2} = -1.5
Graph
Share
Copied to clipboard
\left(x+3\right)\left(x+4\right)\times 4-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Variable x cannot be equal to any of the values -4,-3 since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(x+4\right), the least common multiple of x+4,x+3.
\left(x^{2}+7x+12\right)\times 4-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Use the distributive property to multiply x+3 by x+4 and combine like terms.
4x^{2}+28x+48-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Use the distributive property to multiply x^{2}+7x+12 by 4.
4x^{2}+28x+48-\left(5x+15\right)=\left(x+4\right)\times 3
Use the distributive property to multiply x+3 by 5.
4x^{2}+28x+48-5x-15=\left(x+4\right)\times 3
To find the opposite of 5x+15, find the opposite of each term.
4x^{2}+23x+48-15=\left(x+4\right)\times 3
Combine 28x and -5x to get 23x.
4x^{2}+23x+33=\left(x+4\right)\times 3
Subtract 15 from 48 to get 33.
4x^{2}+23x+33=3x+12
Use the distributive property to multiply x+4 by 3.
4x^{2}+23x+33-3x=12
Subtract 3x from both sides.
4x^{2}+20x+33=12
Combine 23x and -3x to get 20x.
4x^{2}+20x+33-12=0
Subtract 12 from both sides.
4x^{2}+20x+21=0
Subtract 12 from 33 to get 21.
x=\frac{-20±\sqrt{20^{2}-4\times 4\times 21}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 20 for b, and 21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-20±\sqrt{400-4\times 4\times 21}}{2\times 4}
Square 20.
x=\frac{-20±\sqrt{400-16\times 21}}{2\times 4}
Multiply -4 times 4.
x=\frac{-20±\sqrt{400-336}}{2\times 4}
Multiply -16 times 21.
x=\frac{-20±\sqrt{64}}{2\times 4}
Add 400 to -336.
x=\frac{-20±8}{2\times 4}
Take the square root of 64.
x=\frac{-20±8}{8}
Multiply 2 times 4.
x=-\frac{12}{8}
Now solve the equation x=\frac{-20±8}{8} when ± is plus. Add -20 to 8.
x=-\frac{3}{2}
Reduce the fraction \frac{-12}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{28}{8}
Now solve the equation x=\frac{-20±8}{8} when ± is minus. Subtract 8 from -20.
x=-\frac{7}{2}
Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{3}{2} x=-\frac{7}{2}
The equation is now solved.
\left(x+3\right)\left(x+4\right)\times 4-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Variable x cannot be equal to any of the values -4,-3 since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(x+4\right), the least common multiple of x+4,x+3.
\left(x^{2}+7x+12\right)\times 4-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Use the distributive property to multiply x+3 by x+4 and combine like terms.
4x^{2}+28x+48-\left(x+3\right)\times 5=\left(x+4\right)\times 3
Use the distributive property to multiply x^{2}+7x+12 by 4.
4x^{2}+28x+48-\left(5x+15\right)=\left(x+4\right)\times 3
Use the distributive property to multiply x+3 by 5.
4x^{2}+28x+48-5x-15=\left(x+4\right)\times 3
To find the opposite of 5x+15, find the opposite of each term.
4x^{2}+23x+48-15=\left(x+4\right)\times 3
Combine 28x and -5x to get 23x.
4x^{2}+23x+33=\left(x+4\right)\times 3
Subtract 15 from 48 to get 33.
4x^{2}+23x+33=3x+12
Use the distributive property to multiply x+4 by 3.
4x^{2}+23x+33-3x=12
Subtract 3x from both sides.
4x^{2}+20x+33=12
Combine 23x and -3x to get 20x.
4x^{2}+20x=12-33
Subtract 33 from both sides.
4x^{2}+20x=-21
Subtract 33 from 12 to get -21.
\frac{4x^{2}+20x}{4}=-\frac{21}{4}
Divide both sides by 4.
x^{2}+\frac{20}{4}x=-\frac{21}{4}
Dividing by 4 undoes the multiplication by 4.
x^{2}+5x=-\frac{21}{4}
Divide 20 by 4.
x^{2}+5x+\left(\frac{5}{2}\right)^{2}=-\frac{21}{4}+\left(\frac{5}{2}\right)^{2}
Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+5x+\frac{25}{4}=\frac{-21+25}{4}
Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}+5x+\frac{25}{4}=1
Add -\frac{21}{4} to \frac{25}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+\frac{5}{2}\right)^{2}=1
Factor x^{2}+5x+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{1}
Take the square root of both sides of the equation.
x+\frac{5}{2}=1 x+\frac{5}{2}=-1
Simplify.
x=-\frac{3}{2} x=-\frac{7}{2}
Subtract \frac{5}{2} from both sides of the equation.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}