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Simplifying 81 = x2 + 17.3x Reorder the terms: 81 = 17.3x + x2 Solving 81 = 17.3x + x2 Solving for variable 'x'. Reorder the terms: 81 + -17.3x + -1x2 = 17.3x + -17.3x + x2 + -1x2 Combine like terms: 17.3x + -17.3x = 0.0 81 + -17.3x + -1x2 = 0.0 + x2 + -1x2 81 + -17.3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -17.3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 17.3x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 17.3x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 17.3x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 17.3x + x2 = 0 + 81 17.3x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 17.3x + x2 = 81 The x term is 17.3x. Take half its coefficient (8.65). Square it (74.8225) and add it to both sides. Add '74.8225' to each side of the equation. 17.3x + 74.8225 + x2 = 81 + 74.8225 Reorder the terms: 74.8225 + 17.3x + x2 = 81 + 74.8225 Combine like terms: 81 + 74.8225 = 155.8225 74.8225 + 17.3x + x2 = 155.8225 Factor a perfect square on the left side: (x + 8.65)(x + 8.65) = 155.8225 Calculate the square root of the right side: 12.482888288 Break this problem into two subproblems by setting (x + 8.65) equal to 12.482888288 and -12.482888288.Subproblem 1
x + 8.65 = 12.482888288 Simplifying x + 8.65 = 12.482888288 Reorder the terms: 8.65 + x = 12.482888288 Solving 8.65 + x = 12.482888288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.65' to each side of the equation. 8.65 + -8.65 + x = 12.482888288 + -8.65 Combine like terms: 8.65 + -8.65 = 0.00 0.00 + x = 12.482888288 + -8.65 x = 12.482888288 + -8.65 Combine like terms: 12.482888288 + -8.65 = 3.832888288 x = 3.832888288 Simplifying x = 3.832888288Subproblem 2
x + 8.65 = -12.482888288 Simplifying x + 8.65 = -12.482888288 Reorder the terms: 8.65 + x = -12.482888288 Solving 8.65 + x = -12.482888288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.65' to each side of the equation. 8.65 + -8.65 + x = -12.482888288 + -8.65 Combine like terms: 8.65 + -8.65 = 0.00 0.00 + x = -12.482888288 + -8.65 x = -12.482888288 + -8.65 Combine like terms: -12.482888288 + -8.65 = -21.132888288 x = -21.132888288 Simplifying x = -21.132888288Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.832888288, -21.132888288}
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