Solve (2x-9)(2x+9) - Socratic AI (ScanMath)

Pergunta

Simplify the expression

4 x^{2} - 81

Evaluate

(2 x - 9) (2 x + 9)

Use (a - b) (a + b) = a^{2} - b^{2} to simplify the product

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

Evaluate the power

Mais Passos

Evaluate

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

4 x^{2} - 9^{2}

Solução

4 x^{2} - 81

Mostrar solução

x_{1} = - \frac{9}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 4.5, x_{2} = 4.5

Evaluate

(2 x - 9) (2 x + 9)

To find the roots of the expression,set the expression equal to 0

(2 x - 9) (2 x + 9) = 0

Separate the equation into 2 possible cases

2 x - 9 = 0 2 x + 9 = 0

Solve the equation

Mais Passos

Evaluate

2 x - 9 = 0

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

2 x = 0 + 9

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

2 x = 9

Divide both sides

\frac{2 x}{2} = \frac{9}{2}

Divide the numbers

x = \frac{9}{2}

x = \frac{9}{2} 2 x + 9 = 0

Solve the equation

Mais Passos

Evaluate

2 x + 9 = 0

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

2 x = 0 - 9

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

2 x = - 9

Divide both sides

\frac{2 x}{2} = \frac{- 9}{2}

Divide the numbers

x = \frac{- 9}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{9}{2}

x = \frac{9}{2} x = - \frac{9}{2}

Solução

x_{1} = - \frac{9}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 4.5, x_{2} = 4.5

Mostrar solução