Solve (2x-3)^(2)+(5x+2)(x-1)=(3x-1)^(2)-5(x-2)+16 | 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

$${ \left(2x-3 \right) }^{ 2 } +(5x+2)(x-1)= { \left(3x-1 \right) }^{ 2 } -5(x-2)+16$$

Solve for x

$x=-5$

Steps for Solving Linear Equation

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-3\right)^{2}$.

$$4x^{2}-12x+9+\left(5x+2\right)\left(x-1\right)=\left(3x-1\right)^{2}-5\left(x-2\right)+16$$

Use the distributive property to multiply $5x+2$ by $x-1$ and combine like terms.

$$4x^{2}-12x+9+5x^{2}-3x-2=\left(3x-1\right)^{2}-5\left(x-2\right)+16$$

Combine $4x^{2}$ and $5x^{2}$ to get $9x^{2}$.

$$9x^{2}-12x+9-3x-2=\left(3x-1\right)^{2}-5\left(x-2\right)+16$$

Combine $-12x$ and $-3x$ to get $-15x$.

$$9x^{2}-15x+9-2=\left(3x-1\right)^{2}-5\left(x-2\right)+16$$

Subtract $2$ from $9$ to get $7$.

$$9x^{2}-15x+7=\left(3x-1\right)^{2}-5\left(x-2\right)+16$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(3x-1\right)^{2}$.

$$9x^{2}-15x+7=9x^{2}-6x+1-5\left(x-2\right)+16$$

Use the distributive property to multiply $-5$ by $x-2$.

$$9x^{2}-15x+7=9x^{2}-6x+1-5x+10+16$$

Combine $-6x$ and $-5x$ to get $-11x$.

$$9x^{2}-15x+7=9x^{2}-11x+1+10+16$$

Add $1$ and $10$ to get $11$.

$$9x^{2}-15x+7=9x^{2}-11x+11+16$$

Add $11$ and $16$ to get $27$.

$$9x^{2}-15x+7=9x^{2}-11x+27$$

Subtract $9x^{2}$ from both sides.

$$9x^{2}-15x+7-9x^{2}=-11x+27$$

Combine $9x^{2}$ and $-9x^{2}$ to get $0$.

$$-15x+7=-11x+27$$

Add $11x$ to both sides.

$$-15x+7+11x=27$$

Combine $-15x$ and $11x$ to get $-4x$.

$$-4x+7=27$$

Subtract $7$ from both sides.

$$-4x=27-7$$

Subtract $7$ from $27$ to get $20$.

$$-4x=20$$

Divide both sides by $-4$.

$$x=\frac{20}{-4}$$

Divide $20$ by $-4$ to get $-5$.

$$x=-5$$