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Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : -2*x^2-(-4)=0
3.1 Pull out like factors : 4 - 2x2 = -2 • (x2 - 2)
3.2 Factoring: x2 - 2 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 : 2 is not a square !!Ruling : Binomial can not be factored as the difference of two perfect squares.
4.1 Solve : -2 = 0This equation has no solution.A a non-zero constant never equals zero.
4.2 Solve : x2-2 = 0 Add 2 to both sides of the equation : x2 = 2 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 2 The equation has two real solutions These solutions are x = ± √2 = ± 1.4142
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