(x-3)%3D37.jpeg "(2x+7)(x-3)=37")
Solving the Equation (2x + 7)(x - 3) = 37
This article will guide you through the steps of solving the equation (2x + 7)(x - 3) = 37.
Expanding the Equation
First, we need to expand the left side of the equation by multiplying the two binomials. Using the FOIL method (First, Outer, Inner, Last), we get:
2x² - 6x + 7x - 21 = 37
Combining like terms, we get:
2x² + x - 21 = 37
Rearranging the Equation
Next, we need to rearrange the equation to set it equal to zero:
2x² + x - 58 = 0
Solving the Quadratic Equation
Now we have a quadratic equation in standard form (ax² + bx + c = 0). We can solve this using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = 1, and c = -58. Plugging these values into the quadratic formula, we get:
x = (-1 ± √(1² - 4 * 2 * -58)) / (2 * 2)
Simplifying the expression, we get:
x = (-1 ± √(465)) / 4
Therefore, the solutions to the equation are:
x = (-1 + √465) / 4
x = (-1 - √465) / 4
These are the two values of x that satisfy the original equation.
Conclusion
We have successfully solved the equation (2x + 7)(x - 3) = 37. The solutions are x = (-1 + √465) / 4 and x = (-1 - √465) / 4.