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Simplifying X2 + 20X + 100 = 12 Reorder the terms: 100 + 20X + X2 = 12 Solving 100 + 20X + X2 = 12 Solving for variable 'X'. Reorder the terms: 100 + -12 + 20X + X2 = 12 + -12 Combine like terms: 100 + -12 = 88 88 + 20X + X2 = 12 + -12 Combine like terms: 12 + -12 = 0 88 + 20X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-88' to each side of the equation. 88 + 20X + -88 + X2 = 0 + -88 Reorder the terms: 88 + -88 + 20X + X2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + 20X + X2 = 0 + -88 20X + X2 = 0 + -88 Combine like terms: 0 + -88 = -88 20X + X2 = -88 The X term is 20X. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20X + 100 + X2 = -88 + 100 Reorder the terms: 100 + 20X + X2 = -88 + 100 Combine like terms: -88 + 100 = 12 100 + 20X + X2 = 12 Factor a perfect square on the left side: (X + 10)(X + 10) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (X + 10) equal to 3.464101615 and -3.464101615.Subproblem 1
X + 10 = 3.464101615 Simplifying X + 10 = 3.464101615 Reorder the terms: 10 + X = 3.464101615 Solving 10 + X = 3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + X = 3.464101615 + -10 Combine like terms: 10 + -10 = 0 0 + X = 3.464101615 + -10 X = 3.464101615 + -10 Combine like terms: 3.464101615 + -10 = -6.535898385 X = -6.535898385 Simplifying X = -6.535898385Subproblem 2
X + 10 = -3.464101615 Simplifying X + 10 = -3.464101615 Reorder the terms: 10 + X = -3.464101615 Solving 10 + X = -3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + X = -3.464101615 + -10 Combine like terms: 10 + -10 = 0 0 + X = -3.464101615 + -10 X = -3.464101615 + -10 Combine like terms: -3.464101615 + -10 = -13.464101615 X = -13.464101615 Simplifying X = -13.464101615Solution
The solution to the problem is based on the solutions from the subproblems. X = {-6.535898385, -13.464101615}
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