Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.5 - 2x^2 = -15
Accepted Solution
A:
5-2x2=-15 Two solutions were found : x = ± √10 = ± 3.1623Rearrange:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 5-2*x^2-(-15)=0 Step by step solution :Step 1 :Equation at the end of step 1 : (5 - 2x2) - -15 = 0 Step 2 :Step 3 :Pulling out like terms : 3.1 Pull out like factors : 20 - 2x2 = -2 • (x2 - 10) Trying to factor as a Difference of Squares : 3.2 Factoring: x2 - 10 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication.Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 10 is not a square !!Ruling : Binomial can not be factored as the difference of two perfect squares.Equation at the end of step 3 : -2 • (x2 - 10) = 0 Step 4 :Equations which are never true : 4.1 Solve : -2 = 0This equation has no solution.A a non-zero constant never equals zero.Solving a Single Variable Equation : 4.2 Solve : x2-10 = 0 Add 10 to both sides of the equation : x2 = 10 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 10 The equation has two real solutions These solutions are x = ± √10 = ± 3.1623 Two solutions were found : x = ± √10 = ± 3.1623