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We can use the methods for solving quadratic equations that we learned in this section to solve for the missing side. You can use the quadratic formula to solve quadratic equations that previously you solved by factoring. Because each of the terms is squared in the theorem, when we are solving for a side of a triangle, we have a quadratic equation. As you can see, you can now solve quadratic equations that would not be ones that you could factor using our previous factoring techniques. We may however, be given a quadratic equation that is not in this form and so our first step is to rewrite the equation into this standard form. We use the Pythagorean Theorem to solve for the length of one side of a triangle when we have the lengths of the other two. Equations that can be rearranged to be a quadratic equation in standard form The standard form for a quadratic equation is ax2 + bx + c 0, a 0. It has immeasurable uses in architecture, engineering, the sciences, geometry, trigonometry, and algebra, and in everyday applications. Remember the helpful saying: The angry bee is deciding whether or not to go into the house where the other bees are square dancing and losing to 4 aces at the party that is all over at 2 am. mc-TY-quadeqns-1 This unit is about the solution of quadratic equations. Introduction This unit is about how to solve quadratic equations. Solving quadratic equations by using graphs 7 1 c mathcentre 2009. Solving quadratic equations using a formula 6 5. 1 2(4) 2 22 4 Add (1 2)2 to both sides of the equal sign and simplify the right side. First, Memorize the Quadratic Formula: The quadratic equation ax2 + b x + c 0 has solution a b b ac x 2 ± 2 4. Solving quadratic equations by completing the square 5 4. x2 + 4x + 1 0 x2 + 4x 1 Multiply the b term by 1 2 and square it. It is based on a right triangle, and states the relationship among the lengths of the sides as \(a^2+b^2=c^2\), where \(a\) and \(b\) refer to the legs of a right triangle adjacent to the \(90°\) angle, and \(c\) refers to the hypotenuse. Given a quadratic equation that cannot be factored, and with a 1, first add or subtract the constant term to the right sign of the equal sign. One of the most famous formulas in mathematics is the Pythagorean Theorem.