The list of steps, in order, that will solve the equation is:
- Addition of 5 to both sides to eliminate the value of -5
- Division of both sides of the equation by 2 to eliminate the coefficient of 2 from the left-hand side
- Taking the square root of both sides
- subtract 3/4 from each side
- Convert the answer to decimal
The given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.
What is a quadratic equation?
A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.
From the parameters given:
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]
- Addition of +5 to both sides
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]
[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]
- Division of both sides by 2
[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]
- Taking the square root of both sides
[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]
- Subtract 3/4 from both sides
[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]
[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]
Learn more about quadratic equations here:
https://brainly.com/question/17210919
