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What are the solutions of the equation 4x^2 + x = -3 ?

Question:

What are the solutions of the equation {eq}4x^2 + x = -3 {/eq}?

Quadratic Formula

The quadratic formula is used to determine the zeros of the second-degree polynomials. The general expression for the quadratic equation {eq}a{x^2} + bx + c = 0 {/eq}, and the solution for the quadratic equation is {eq}x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} {/eq}, where the constants are {eq}a {/eq}, {eq}b {/eq} and {eq}c {/eq}.

Answer and Explanation:


Given Data

  • The quadratic equation is: {eq}4{x^2} + x = - 3 {/eq}


Find the solution of the quadratic equation using the quadratic formula.

{eq}\begin{align*} 4{x^2} + x &= - 3\\ 4{x^2} + x + 3 &= 0\\ x &= \dfrac{{ - \left( 1 \right) \pm \sqrt {{{\left( 1 \right)}^2} - 4\left( 4 \right)\left( 3 \right)} }}{{2\left( 4 \right)}}\\ x &= \dfrac{{ - 1 \pm \sqrt { - 47} }}{8}\\ x &= \dfrac{{ - 1 \pm \sqrt {47} i}}{8} \end{align*} {/eq}


Thus, the solutions of the quadratic equation is {eq}x = \dfrac{{ - 1 \pm \sqrt {47} i}}{8} {/eq}.


Learn more about this topic:

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The Quadratic Formula: Definition & Example

from Remedial Algebra I

Chapter 25 / Lesson 10
11K

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