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Simplifying 18x2 + -9x + -10 = 0 Reorder the terms: -10 + -9x + 18x2 = 0 Solving -10 + -9x + 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'. -0.5555555556 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.5x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.5x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.5555555556 -0.5x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.5x + x2 = 0.5555555556 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.5555555556 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.5555555556 + 0.0625 Combine like terms: 0.5555555556 + 0.0625 = 0.6180555556 0.0625 + -0.5x + x2 = 0.6180555556 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.6180555556 Calculate the square root of the right side: 0.786165094 Break this problem into two subproblems by setting (x + -0.25) equal to 0.786165094 and -0.786165094.Subproblem 1
x + -0.25 = 0.786165094 Simplifying x + -0.25 = 0.786165094 Reorder the terms: -0.25 + x = 0.786165094 Solving -0.25 + x = 0.786165094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.786165094 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.786165094 + 0.25 x = 0.786165094 + 0.25 Combine like terms: 0.786165094 + 0.25 = 1.036165094 x = 1.036165094 Simplifying x = 1.036165094Subproblem 2
x + -0.25 = -0.786165094 Simplifying x + -0.25 = -0.786165094 Reorder the terms: -0.25 + x = -0.786165094 Solving -0.25 + x = -0.786165094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.786165094 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.786165094 + 0.25 x = -0.786165094 + 0.25 Combine like terms: -0.786165094 + 0.25 = -0.536165094 x = -0.536165094 Simplifying x = -0.536165094Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036165094, -0.536165094}
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