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Simplifying 10X2 + 1X + -10 = 0 Reorder the terms: -10 + 1X + 10X2 = 0 Solving -10 + 1X + 10X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1 + 0.1X + X2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1X + X2 = 0 + 1 0.1X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1X + X2 = 1 The X term is 0.1X. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1X + 0.0025 + X2 = 1 + 0.0025 Reorder the terms: 0.0025 + 0.1X + X2 = 1 + 0.0025 Combine like terms: 1 + 0.0025 = 1.0025 0.0025 + 0.1X + X2 = 1.0025 Factor a perfect square on the left side: (X + 0.05)(X + 0.05) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (X + 0.05) equal to 1.00124922 and -1.00124922.Subproblem 1
X + 0.05 = 1.00124922 Simplifying X + 0.05 = 1.00124922 Reorder the terms: 0.05 + X = 1.00124922 Solving 0.05 + X = 1.00124922 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + X = 1.00124922 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + X = 1.00124922 + -0.05 X = 1.00124922 + -0.05 Combine like terms: 1.00124922 + -0.05 = 0.95124922 X = 0.95124922 Simplifying X = 0.95124922Subproblem 2
X + 0.05 = -1.00124922 Simplifying X + 0.05 = -1.00124922 Reorder the terms: 0.05 + X = -1.00124922 Solving 0.05 + X = -1.00124922 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + X = -1.00124922 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + X = -1.00124922 + -0.05 X = -1.00124922 + -0.05 Combine like terms: -1.00124922 + -0.05 = -1.05124922 X = -1.05124922 Simplifying X = -1.05124922Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.95124922, -1.05124922}
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