Solve (x - 4) ^ 2 + 8 = 0 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(x-4)^{2}+8=0$$

Solve for x (complex solution)

$x=-2\sqrt{2}i+4\approx 4-2.828427125i$
$x=4+2\sqrt{2}i\approx 4+2.828427125i$

Steps by Finding Square Root

Subtracting $8$ from itself leaves $0$.

$$\left(x-4\right)^{2}=-8$$

Take the square root of both sides of the equation.

$$x-4=2\sqrt{2}i$$ $$x-4=-2\sqrt{2}i$$

Add $4$ to both sides of the equation.

$$x-4-\left(-4\right)=2\sqrt{2}i-\left(-4\right)$$ $$x-4-\left(-4\right)=-2\sqrt{2}i-\left(-4\right)$$

Subtracting $-4$ from itself leaves $0$.

$$x=2\sqrt{2}i-\left(-4\right)$$ $$x=-2\sqrt{2}i-\left(-4\right)$$

Subtract $-4$ from $2i\sqrt{2}$.

$$x=4+2\sqrt{2}i$$

Subtract $-4$ from $-2i\sqrt{2}$.

$$x=-2\sqrt{2}i+4$$

The equation is now solved.

$$x=4+2\sqrt{2}i$$ $$x=-2\sqrt{2}i+4$$