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Simplifying 81x2 + 90x = 175 Reorder the terms: 90x + 81x2 = 175 Solving 90x + 81x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + 90x + 81x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 90x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -2.160493827 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '2.160493827' to each side of the equation. -2.160493827 + 1.111111111x + 2.160493827 + x2 = 0 + 2.160493827 Reorder the terms: -2.160493827 + 2.160493827 + 1.111111111x + x2 = 0 + 2.160493827 Combine like terms: -2.160493827 + 2.160493827 = 0.000000000 0.000000000 + 1.111111111x + x2 = 0 + 2.160493827 1.111111111x + x2 = 0 + 2.160493827 Combine like terms: 0 + 2.160493827 = 2.160493827 1.111111111x + x2 = 2.160493827 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 2.160493827 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 2.160493827 + 0.3086419752 Combine like terms: 2.160493827 + 0.3086419752 = 2.4691358022 0.3086419752 + 1.111111111x + x2 = 2.4691358022 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 2.4691358022 Calculate the square root of the right side: 1.571348403 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.571348403 and -1.571348403.Subproblem 1
x + 0.5555555555 = 1.571348403 Simplifying x + 0.5555555555 = 1.571348403 Reorder the terms: 0.5555555555 + x = 1.571348403 Solving 0.5555555555 + x = 1.571348403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.571348403 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.571348403 + -0.5555555555 x = 1.571348403 + -0.5555555555 Combine like terms: 1.571348403 + -0.5555555555 = 1.0157928475 x = 1.0157928475 Simplifying x = 1.0157928475Subproblem 2
x + 0.5555555555 = -1.571348403 Simplifying x + 0.5555555555 = -1.571348403 Reorder the terms: 0.5555555555 + x = -1.571348403 Solving 0.5555555555 + x = -1.571348403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.571348403 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.571348403 + -0.5555555555 x = -1.571348403 + -0.5555555555 Combine like terms: -1.571348403 + -0.5555555555 = -2.1269039585 x = -2.1269039585 Simplifying x = -2.1269039585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0157928475, -2.1269039585}
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