Solve 4x^2=2x-2=6x^2-5x 1

Question

Solve the system of equations

x \in / R

Alternative Form

No real solution

Evaluate

{4 x^{2} = 2 x - 2 2 x - 2 = 6 x^{2} - 5 x \times 1

Calculate

More Steps

Evaluate

4 x^{2} = 2 x - 2

Move the expression to the left side

4 x^{2} - (2 x - 2) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

4 x^{2} - 2 x + 2 = 0

Substitute a= 4,b= - 2 and c= 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 4 \times 2}{2 \times 4}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 4 \times 2}{8}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 \times 4 \times 2

Multiply the terms

(- 2)^{2} - 32

Rewrite the expression

2^{2} - 32

Evaluate the power

4 - 32

Subtract the numbers

- 28

x = \frac{2 \pm - 28}{8}

The expression is undefined in the set of real numbers

x \in / R

{x \in / R 2 x - 2 = 6 x^{2} - 5 x \times 1

Calculate

More Steps

Evaluate

2 x - 2 = 6 x^{2} - 5 x \times 1

Multiply the terms

2 x - 2 = 6 x^{2} - 5 x

Move the expression to the left side

2 x - 2 - (6 x^{2} - 5 x) = 0

Subtract the terms

More Steps

Evaluate

2 x - 2 - (6 x^{2} - 5 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x - 2 - 6 x^{2} + 5 x

Add the terms

7 x - 2 - 6 x^{2}

7 x - 2 - 6 x^{2} = 0

Factor the expression

More Steps

Evaluate

7 x - 2 - 6 x^{2}

Reorder the terms

- 2 + 7 x - 6 x^{2}

Rewrite the expression

- 2 + (3 + 4) x - 6 x^{2}

Calculate

- 2 + 3 x + 4 x - 6 x^{2}

Rewrite the expression

- 2 + 3 x + 2 x \times 2 - 2 x \times 3 x

Factor out - 1 from the expression

- (2 - 3 x) + 2 x \times 2 - 2 x \times 3 x

Factor out 2 x from the expression

- (2 - 3 x) + 2 x (2 - 3 x)

Factor out 2 - 3 x from the expression

(- 1 + 2 x) (2 - 3 x)

(- 1 + 2 x) (2 - 3 x) = 0

When the product of factors equals 0,at least one factor is 0

- 1 + 2 x = 0 2 - 3 x = 0

Solve the equation for x

More Steps

Evaluate

- 1 + 2 x = 0

Move the constant to the right-hand side and change its sign

2 x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} 2 - 3 x = 0

Solve the equation for x

More Steps

Evaluate

2 - 3 x = 0

Move the constant to the right-hand side and change its sign

- 3 x = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 3 x = - 2

Change the signs on both sides of the equation

3 x = 2

Divide both sides

\frac{3 x}{3} = \frac{2}{3}

Divide the numbers

x = \frac{2}{3}

x = \frac{1}{2} x = \frac{2}{3}

Calculate

x = \frac{1}{2} \cup x = \frac{2}{3}

{x \in / R x = \frac{1}{2} \cup x = \frac{2}{3}

Solution

x \in / R

Alternative Form

No real solution

Show Solution