Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(11x^2-x=10x^2-9x\)
- \(-2(6x^2+9x)=-(10x^2+17x)\)
- \(-8x^2-14x=-3x^2-10x\)
- \(5(-2x^2+9x)=-(18x^2-55x)\)
- \(-5(3x^2+4x)=-(21x^2-3x)\)
- \(x^2+13x=0\)
- \(-2x^2+4x=2x^2-3x\)
- \(-11x^2-3x=-4x^2+8x\)
- \(-4x^2-13x=-5x^2-10x\)
- \(5x^2-7x=0\)
- \(-2(4x^2+3x)=-(14x^2-9x)\)
- \(x^2-5x=-7x^2-2x\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(11x^2-x=10x^2-9x \\ \Leftrightarrow x^2+8x=0 \\
\Leftrightarrow x(x+8) = 0 \\
\Leftrightarrow x = 0 \vee x+8=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-8}{1} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
- \(-2(6x^2+9x)=-(10x^2+17x) \\ \Leftrightarrow -12x^2-18x=-10x^2-17x \\
\Leftrightarrow -12x^2-18x+10x^2+17x= 0 \\
\Leftrightarrow -2x^2+1x=0 \\
\Leftrightarrow x(-2x+1) = 0 \\
\Leftrightarrow x = 0 \vee -2x+1=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-1}{-2} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
- \(-8x^2-14x=-3x^2-10x \\ \Leftrightarrow -5x^2-4x=0 \\
\Leftrightarrow x(-5x-4) = 0 \\
\Leftrightarrow x = 0 \vee -5x-4=0 \\
\Leftrightarrow x = 0 \vee x = \frac{4}{-5} = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
- \(5(-2x^2+9x)=-(18x^2-55x) \\ \Leftrightarrow -10x^2+45x=-18x^2+55x \\
\Leftrightarrow -10x^2+45x+18x^2-55x= 0 \\
\Leftrightarrow 8x^2+10x=0 \\
\Leftrightarrow x(8x+10) = 0 \\
\Leftrightarrow x = 0 \vee 8x+10=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
- \(-5(3x^2+4x)=-(21x^2-3x) \\ \Leftrightarrow -15x^2-20x=-21x^2+3x \\
\Leftrightarrow -15x^2-20x+21x^2-3x= 0 \\
\Leftrightarrow 6x^2+23x=0 \\
\Leftrightarrow x(6x+23) = 0 \\
\Leftrightarrow x = 0 \vee 6x+23=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
- \(x^2+13x=0 \\
\Leftrightarrow x(x+13) = 0 \\
\Leftrightarrow x = 0 \vee x+13=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-13}{1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
- \(-2x^2+4x=2x^2-3x \\ \Leftrightarrow -4x^2+7x=0 \\
\Leftrightarrow x(-4x+7) = 0 \\
\Leftrightarrow x = 0 \vee -4x+7=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-7}{-4} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
- \(-11x^2-3x=-4x^2+8x \\ \Leftrightarrow -7x^2-11x=0 \\
\Leftrightarrow x(-7x-11) = 0 \\
\Leftrightarrow x = 0 \vee -7x-11=0 \\
\Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
- \(-4x^2-13x=-5x^2-10x \\ \Leftrightarrow x^2-3x=0 \\
\Leftrightarrow x(x-3) = 0 \\
\Leftrightarrow x = 0 \vee x-3=0 \\
\Leftrightarrow x = 0 \vee x = \frac{3}{1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
- \(5x^2-7x=0 \\
\Leftrightarrow x(5x-7) = 0 \\
\Leftrightarrow x = 0 \vee 5x-7=0 \\
\Leftrightarrow x = 0 \vee x = \frac{7}{5} \\ V = \Big\{ \frac{7}{5}; 0 \Big\} \\ -----------------\)
- \(-2(4x^2+3x)=-(14x^2-9x) \\ \Leftrightarrow -8x^2-6x=-14x^2+9x \\
\Leftrightarrow -8x^2-6x+14x^2-9x= 0 \\
\Leftrightarrow 6x^2+15x=0 \\
\Leftrightarrow x(6x+15) = 0 \\
\Leftrightarrow x = 0 \vee 6x+15=0 \\
\Leftrightarrow x = 0 \vee x = \frac{-15}{6} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
- \(x^2-5x=-7x^2-2x \\ \Leftrightarrow 8x^2-3x=0 \\
\Leftrightarrow x(8x-3) = 0 \\
\Leftrightarrow x = 0 \vee 8x-3=0 \\
\Leftrightarrow x = 0 \vee x = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)