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Question Number 123143 by aurpeyz last updated on 23/Nov/20

$$write{ax}^2+bx+casasumordifference$$$$oftwosquares$$

Commented by mr W last updated on 23/Nov/20

$$={\left(\sqrt{a}x\right)}^2+2\left(\frac{b}{2\sqrt{a}}\times \sqrt{a}\right)x+{\left(\frac{b}{2\sqrt{a}}\right)}^2+c-\frac{b^2}{4a}$$$$={(\sqrt{a}x+\frac{b}{2\sqrt{a}})}^2-{\left(\sqrt{\frac{b^2}{4a}-c}\right)}^{2}forc<\frac{b^2}{4a}$$$$={(\sqrt{a}x+\frac{b}{2\sqrt{a}})}^2+{\left(\sqrt{c-\frac{b^2}{4a}}\right)}^{2}forc⩾\frac{b^2}{4a}$$

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