When you enter an equation into the calculator, the calculator will begin by expanding (simplifying) the problem. Next, it will attempt to solve the equation by using one or more of the following: addition, subtraction, division, factoring, and completing Any lowercase letter may be used as a variable. Exponents are supported on variables using the ^ (caret) symbol. For example, to express x2, enter x^2. Note: exponents must be positive integers, no negatives, decimals, or variables. Exponents may not be placed on numbers, brackets, or Parentheses ( ) and brackets [ ] may be
used to group terms as in a standard equation or expression. For addition and subtraction, use the standard + and – symbols respectively. For multiplication, use the * symbol. A * symbol is not necessary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x The calculator follows the standard order of operations taught by most algebra books – Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The only exception is that division is not supported; attempts to use the / symbol The above features are not supported. Step 1 Add to both sides of the equation. Step 2 To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of . Step 3 Add the term to each side of the equation. Step 5 Factor the perfect trinomial square into . Step 6 Take the specified root of both sides of the equation to eliminate the exponent on the left side. Pull terms out from under the radical, assuming positive real numbers. The complete solution is the result of both the positive and negative portions of the solution. First, use the positive value of the to find the first solution. Move all terms not containing to the right side of the equation. Subtract from both sides of the equation. Next, use the negative value of the to find the second solution. Move all terms not containing to the right side of the equation. Subtract from both sides of the equation. The complete solution is the result of both the positive and negative portions of the solution.
Complete squares step by stepThe calculator will try to complete the square for the given quadratic expression, ellipse, hyperbola, or any polynomial expression, with steps shown. SolutionYour input: complete the square in $$$x^{2} - 4 x + 5 y^{2} + 10 y + 14$$$. Add and subtract $$$5$$$: $$$x^{2} - 4 x + 5 y^{2} + 10 y + 14=x^{2} - 4 x + 5 y^{2} + 10 y + 14 + \color{red}{\left(5\right)} - \color{red}{\left(5\right)}$$$ Factor $$$5$$$: $$$x^{2} - 4 x + 9 + \color{red}{\left(5 y^{2} + 10 y + 5\right)}=x^{2} - 4 x + 9 + \color{red}{\left(5 \left(y^{2} + 2 y + 1\right)\right)}$$$ Complete the square: $$$x^{2} - 4 x + 9 + 5 \color{red}{\left(y^{2} + 2 y + 1\right)}=x^{2} - 4 x + 9 + 5 \color{red}{\left(y + 1\right)^{2}}$$$ Add and subtract $$$4$$$: $$$x^{2} - 4 x + 5 \left(y + 1\right)^{2} + 9=x^{2} - 4 x + 5 \left(y + 1\right)^{2} + 9 + \color{red}{\left(4\right)} - \color{red}{\left(4\right)}$$$ Complete the square: $$$5 \left(y + 1\right)^{2} + 5 + \color{red}{\left(x^{2} - 4 x + 4\right)}=5 \left(y + 1\right)^{2} + 5 + \color{red}{\left(x - 2\right)^{2}}$$$ Answer: $$$x^{2} - 4 x + 5 y^{2} + 10 y + 14=\left(x - 2\right)^{2} + 5 \left(y + 1\right)^{2} + 5$$$. |
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