Question

Solve the equation.

$2x^2+7x-5=-1$

Short answer

The solutions of the given equation are $x=-4,\frac{1}{2}$.

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Write the standard form of a quadratic equation.

The standard form of a quadratic equation is given by

$a{x}^2+bx+c=0$, where$a\ne 0$

Step 3. Solve the equation 2x2+7x−5=−1.

$$\begin{gathered} 2x^2+7x-5=-1 \\ 2x^2+7x-5+1=0 \\ 2x^2+7x-4=0 \\ 2x^2+8x-x-4=0 \\ 2x\left(x+4\right)-1\left(x+4\right)=0 \\ \left(x+4\right)\left(2x-1\right)=0 \end{gathered}$$

$x+4=0$or$2x-1=0$

$x=-4$or$2x=1$

$x=-4$or$x=\frac{1}{2}$

$x=-4,\frac{1}{2}$

Therefore the solutions of the given equation are $x=-4,\frac{1}{2}$.