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Simplifying x2 + 10x + -10095 = 0 Reorder the terms: -10095 + 10x + x2 = 0 Solving -10095 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10095' to each side of the equation. -10095 + 10x + 10095 + x2 = 0 + 10095 Reorder the terms: -10095 + 10095 + 10x + x2 = 0 + 10095 Combine like terms: -10095 + 10095 = 0 0 + 10x + x2 = 0 + 10095 10x + x2 = 0 + 10095 Combine like terms: 0 + 10095 = 10095 10x + x2 = 10095 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 10095 + 25 Reorder the terms: 25 + 10x + x2 = 10095 + 25 Combine like terms: 10095 + 25 = 10120 25 + 10x + x2 = 10120 Factor a perfect square on the left side: (x + 5)(x + 5) = 10120 Calculate the square root of the right side: 100.59821072 Break this problem into two subproblems by setting (x + 5) equal to 100.59821072 and -100.59821072.Subproblem 1
x + 5 = 100.59821072 Simplifying x + 5 = 100.59821072 Reorder the terms: 5 + x = 100.59821072 Solving 5 + x = 100.59821072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 100.59821072 + -5 Combine like terms: 5 + -5 = 0 0 + x = 100.59821072 + -5 x = 100.59821072 + -5 Combine like terms: 100.59821072 + -5 = 95.59821072 x = 95.59821072 Simplifying x = 95.59821072Subproblem 2
x + 5 = -100.59821072 Simplifying x + 5 = -100.59821072 Reorder the terms: 5 + x = -100.59821072 Solving 5 + x = -100.59821072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -100.59821072 + -5 Combine like terms: 5 + -5 = 0 0 + x = -100.59821072 + -5 x = -100.59821072 + -5 Combine like terms: -100.59821072 + -5 = -105.59821072 x = -105.59821072 Simplifying x = -105.59821072Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.59821072, -105.59821072}
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