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Simplifying 18x2 + -2x + -7 = 0 Reorder the terms: -7 + -2x + 18x2 = 0 Solving -7 + -2x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -0.1111111111x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -0.1111111111x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -0.1111111111x + x2 = 0 + 0.3888888889 -0.1111111111x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -0.1111111111x + x2 = 0.3888888889 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 0.3888888889 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 0.3888888889 + 0.003086419752 Combine like terms: 0.3888888889 + 0.003086419752 = 0.391975308652 0.003086419752 + -0.1111111111x + x2 = 0.391975308652 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 0.391975308652 Calculate the square root of the right side: 0.626079315 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 0.626079315 and -0.626079315.Subproblem 1
x + -0.05555555555 = 0.626079315 Simplifying x + -0.05555555555 = 0.626079315 Reorder the terms: -0.05555555555 + x = 0.626079315 Solving -0.05555555555 + x = 0.626079315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 0.626079315 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.626079315 + 0.05555555555 x = 0.626079315 + 0.05555555555 Combine like terms: 0.626079315 + 0.05555555555 = 0.68163487055 x = 0.68163487055 Simplifying x = 0.68163487055Subproblem 2
x + -0.05555555555 = -0.626079315 Simplifying x + -0.05555555555 = -0.626079315 Reorder the terms: -0.05555555555 + x = -0.626079315 Solving -0.05555555555 + x = -0.626079315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -0.626079315 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.626079315 + 0.05555555555 x = -0.626079315 + 0.05555555555 Combine like terms: -0.626079315 + 0.05555555555 = -0.57052375945 x = -0.57052375945 Simplifying x = -0.57052375945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.68163487055, -0.57052375945}
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