Solve (2x-1)^2-(3-x)^2=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 2, x_{2} = 1. \dot{3}

Evaluate

(2 x - 1)^{2} - (3 - x)^{2} = 0

Expand the expression

More Steps

Evaluate

(2 x - 1)^{2} - (3 - x)^{2}

Expand the expression

More Steps

Evaluate

(2 x - 1)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(2 x)^{2} - 2 \times 2 x \times 1 + 1^{2}

Calculate

4 x^{2} - 4 x + 1

4 x^{2} - 4 x + 1 - (3 - x)^{2}

Evaluate the power

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Evaluate

- (3 - x)^{2}

Expand the expression

- (9 - 6 x + x^{2})

Expand the expression

- 9 + 6 x - x^{2}

4 x^{2} - 4 x + 1 - 9 + 6 x - x^{2}

Subtract the terms

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Evaluate

4 x^{2} - x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 1) x^{2}

Subtract the numbers

3 x^{2}

3 x^{2} - 4 x + 1 - 9 + 6 x

Add the terms

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Evaluate

- 4 x + 6 x

Collect like terms by calculating the sum or difference of their coefficients

(- 4 + 6) x

Add the numbers

2 x

3 x^{2} + 2 x + 1 - 9

Subtract the numbers

3 x^{2} + 2 x - 8

3 x^{2} + 2 x - 8 = 0

Factor the expression

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Evaluate

3 x^{2} + 2 x - 8

Rewrite the expression

3 x^{2} + (- 4 + 6) x - 8

Calculate

3 x^{2} - 4 x + 6 x - 8

Rewrite the expression

x \times 3 x - x \times 4 + 2 \times 3 x - 2 \times 4

Factor out x from the expression

x (3 x - 4) + 2 \times 3 x - 2 \times 4

Factor out 2 from the expression

x (3 x - 4) + 2 (3 x - 4)

Factor out 3 x - 4 from the expression

(x + 2) (3 x - 4)

(x + 2) (3 x - 4) = 0

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

3 x - 4 = 0 x + 2 = 0

Solve the equation for x

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Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = \frac{4}{3} x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = \frac{4}{3} x = - 2

Solution

x_{1} = - 2, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 2, x_{2} = 1. \dot{3}

Show Solution

Solve the quadratic equation

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