Find a number whose square diminsted by 119 is equal to ten times th

1.	Find a number whose square diminsted by 119 is equal to ten times the excess of the number over 8.
Answer» $\large\underline{\sf{Solution-}}$ Basic Concept Used :- WRITING System of Equations from Word Problems 1. Understand the PROBLEM. Understand all the words used in stating the problem. Understand what you are asked to find. ... 2. Translate the problem to an equation. Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents. 3. Carry out the plan and solve the problem. Let's solve the problem now!! Let the required NUMBER be 'x'. According to statement, Square of the number diminsted by 119 is equal to ten times the EXCESS of the number over 8. $\rm :\implies\: {x}^{2} - 119 = 10(x - 8)$ $\rm :\longmapsto\: {x}^{2} - 119 = 10x - 80$ $\rm :\longmapsto\: {x}^{2} - 10x - 39 = 0$ $\rm :\longmapsto\: {x}^{2} - 13x + 3x - 39 = 0$ $\rm :\longmapsto\:x(x - 13) + 3(x - 13) = 0$ $\rm :\longmapsto\:(x - 13)(x + 3) = 0$ $\rm :\implies\:x = 13 \: \: \: or \: \: \: x = - 3$ $\overbrace{ \underline { \boxed { \rm \therefore The \: number \: is \:13 \: \: \: \: or \: \: - \: 3 )}}}$