Answer:
[tex]x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
Step-by-step explanation:
Given equation: [tex]5x^2-12=88[/tex]
Step 1: Add 12 to both sides.
[tex]\\\implies 5x^2-12+12=88+12\\\\\implies 5x^2=100[/tex]
Step 2: Divide both sides by 5
[tex]\\\implies\dfrac{5x^2}{5}=\dfrac{100}{5}\\\\\implies x^2=20[/tex]
Step 3: Take the square root of both sides (positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{20}\\\\\implies x=\pm\ \sqrt{20}[/tex]
Step 4: Simplify.
[tex]\\\implies x=\pm\ \sqrt{4\times5}\\\\\implies x=\pm\ 2\sqrt{5}[/tex]
Step 5: Separate into two cases.
[tex]\implies x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
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