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Simplifying (10 + -1x2) = 81x Remove parenthesis around (10 + -1x2) 10 + -1x2 = 81x Solving 10 + -1x2 = 81x Solving for variable 'x'. Reorder the terms: 10 + -81x + -1x2 = 81x + -81x Combine like terms: 81x + -81x = 0 10 + -81x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 81x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 81x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 81x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 81x + x2 = 0 + 10 81x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 81x + x2 = 10 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = 10 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 10 + 1640.25 Combine like terms: 10 + 1640.25 = 1650.25 1640.25 + 81x + x2 = 1650.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1650.25 Calculate the square root of the right side: 40.623269194 Break this problem into two subproblems by setting (x + 40.5) equal to 40.623269194 and -40.623269194.Subproblem 1
x + 40.5 = 40.623269194 Simplifying x + 40.5 = 40.623269194 Reorder the terms: 40.5 + x = 40.623269194 Solving 40.5 + x = 40.623269194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 40.623269194 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 40.623269194 + -40.5 x = 40.623269194 + -40.5 Combine like terms: 40.623269194 + -40.5 = 0.123269194 x = 0.123269194 Simplifying x = 0.123269194Subproblem 2
x + 40.5 = -40.623269194 Simplifying x + 40.5 = -40.623269194 Reorder the terms: 40.5 + x = -40.623269194 Solving 40.5 + x = -40.623269194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -40.623269194 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -40.623269194 + -40.5 x = -40.623269194 + -40.5 Combine like terms: -40.623269194 + -40.5 = -81.123269194 x = -81.123269194 Simplifying x = -81.123269194Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.123269194, -81.123269194}
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