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Simplifying 9x2 + -30 = x Reorder the terms: -30 + 9x2 = x Solving -30 + 9x2 = x Solving for variable 'x'. Reorder the terms: -30 + -1x + 9x2 = x + -1x Combine like terms: x + -1x = 0 -30 + -1x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.333333333 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -0.1111111111x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -0.1111111111x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 3.333333333 -0.1111111111x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -0.1111111111x + x2 = 3.333333333 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 = 3.333333333 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 3.333333333 + 0.003086419752 Combine like terms: 3.333333333 + 0.003086419752 = 3.336419752752 0.003086419752 + -0.1111111111x + x2 = 3.336419752752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 3.336419752752 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.826586914 and -1.826586914.Subproblem 1
x + -0.05555555555 = 1.826586914 Simplifying x + -0.05555555555 = 1.826586914 Reorder the terms: -0.05555555555 + x = 1.826586914 Solving -0.05555555555 + x = 1.826586914 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 = 1.826586914 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.826586914 + 0.05555555555 x = 1.826586914 + 0.05555555555 Combine like terms: 1.826586914 + 0.05555555555 = 1.88214246955 x = 1.88214246955 Simplifying x = 1.88214246955Subproblem 2
x + -0.05555555555 = -1.826586914 Simplifying x + -0.05555555555 = -1.826586914 Reorder the terms: -0.05555555555 + x = -1.826586914 Solving -0.05555555555 + x = -1.826586914 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 = -1.826586914 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.826586914 + 0.05555555555 x = -1.826586914 + 0.05555555555 Combine like terms: -1.826586914 + 0.05555555555 = -1.77103135845 x = -1.77103135845 Simplifying x = -1.77103135845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.88214246955, -1.77103135845}
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