Solving linear and quadratic equations

• Solving quadratic equations by factoring

  1. Factorize the quadratic equation

  2. Set the factorized expression equal to 0

  3. Solve the resulting equations
• Factorizing is required to solve quadratic equations
• Factorizing a quadratic equation

  1. Identify the numbers that multiply to give the constant term

  2. Arrange the factors in a double bracket with the coefficient of x in the middle
• When the quadratic equation is in the form x^2 + bx + c = 0


  The solutions are given by the values of x that make each bracket equal to 0
• The solutions are the values of x where the quadratic curve crosses the x-axis
• If the quadratic equation is not initially equal to 0, it needs to be rearranged to be in the form x^2 + bx + c = 0
• Factorizing a quadratic equation with no constant term

  Take the coefficient of x outside a single bracket
• If a quadratic equation has no constant term, it can be factored into a single bracket
• The solutions for a quadratic equation factored into a single bracket are the value(s) of x that make the bracket equal to 0
• if there is an X or a single bracket a piece on the outside there is just always equal to zero
• the solution x equals zero means the curve crosses through or passes through the origin
• Solving a single bracket equation

  1. Set equal to zero

  2. Solve equation
• one solution is a decimal, it passes through the axes at a decimal value
• Solving a single bracket equation with coefficients

  1. Set equal to 0

  2. Solve equation by flipping sign and dividing
• if we have coefficients of x squared that are greater than zero we need to factorize using a double bracket
• Factorizing a quadratic with x^2 coefficient

  1. Set up double bracket

  2. Determine factors to make correct middle term

  3. Solve each bracket equation
• one solution is a fraction, it passes through the axes at a fractional value
• Solving equations

  1. Reverse the process

  2. Isolate the variable

  3. Divide both sides to find the value of the variable
• When solving equations with fractions, the denominator is locked in and must be removed by multiplying both sides by that value
• If the solution is not a whole number, it can be left as a fraction or simplified to a mixed number