Solve 2x^2+3x | Microsoft Math Solver

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Factor

x (2 x + 3)

Solution Steps

Steps Using the Quadratic Formula

Solution Steps

2 x^{2} + 3 x

Factor out

x

.

x (2 x + 3)

Evaluate

x (2 x + 3)

Graph

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2 x^{2} + 3 x

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x\left(2x+3\right)

Factor out x.

2x^{2}+3x=0

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

x=\frac{-3±\sqrt{3^{2}}}{2\times 2}

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=\frac{-3±3}{2\times 2}

Take the square root of 3^{2}\approx 9.

x=\frac{-3±3}{4}

Multiply 2 times 2.

x=\frac{0}{4}

Now solve the equation x=\frac{-3±3}{4} when ± is plus. Add -3 to 3.

x=0

Divide 0 by 4.

x=\frac{-6}{4}

Now solve the equation x=\frac{-3±3}{4} when ± is minus. Subtract 3 from -3.

x=-\frac{3}{2}

Reduce the fraction \frac{-6}{4}=-1.5 to lowest terms by extracting and canceling out 2.

2x^{2}+3x=2x\left(x-\left(-\frac{3}{2}\right)\right)

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{3}{2}=-1.5 for x_{2}.

2x^{2}+3x=2x\left(x+\frac{3}{2}\right)

Simplify all the expressions of the form p-\left(-q\right) to p+q.

2x^{2}+3x=2x\times \left(\frac{2x+3}{2}\right)

Add \frac{3}{2}=1.5 to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

2x^{2}+3x=x\left(2x+3\right)

Cancel out 2, the greatest common factor in 2 and 2.

Examples

Quadratic equation

x^{2} - 4 x - 5 = 0

4 sin θ cos θ = 2 sin θ

Linear equation

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Simultaneous equation

{8 x + 2 y = 46 7 x + 3 y = 47

Differentiation

\frac{d}{d x} \frac{( 3 x ^{2} - 2 )}{( x - 5 )}

\int_{0}^{1} x e^{- x^{2}} d x

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}

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