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Simplifying 18x2 + 11x + -3 = 0 Reorder the terms: -3 + 11x + 18x2 = 0 Solving -3 + 11x + 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'. -0.1666666667 + 0.6111111111x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.6111111111x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.6111111111x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.6111111111x + x2 = 0 + 0.1666666667 0.6111111111x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.6111111111x + x2 = 0.1666666667 The x term is 0.6111111111x. Take half its coefficient (0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. 0.6111111111x + 0.09336419756 + x2 = 0.1666666667 + 0.09336419756 Reorder the terms: 0.09336419756 + 0.6111111111x + x2 = 0.1666666667 + 0.09336419756 Combine like terms: 0.1666666667 + 0.09336419756 = 0.26003086426 0.09336419756 + 0.6111111111x + x2 = 0.26003086426 Factor a perfect square on the left side: (x + 0.3055555556)(x + 0.3055555556) = 0.26003086426 Calculate the square root of the right side: 0.509932215 Break this problem into two subproblems by setting (x + 0.3055555556) equal to 0.509932215 and -0.509932215.Subproblem 1
x + 0.3055555556 = 0.509932215 Simplifying x + 0.3055555556 = 0.509932215 Reorder the terms: 0.3055555556 + x = 0.509932215 Solving 0.3055555556 + x = 0.509932215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = 0.509932215 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = 0.509932215 + -0.3055555556 x = 0.509932215 + -0.3055555556 Combine like terms: 0.509932215 + -0.3055555556 = 0.2043766594 x = 0.2043766594 Simplifying x = 0.2043766594Subproblem 2
x + 0.3055555556 = -0.509932215 Simplifying x + 0.3055555556 = -0.509932215 Reorder the terms: 0.3055555556 + x = -0.509932215 Solving 0.3055555556 + x = -0.509932215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = -0.509932215 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = -0.509932215 + -0.3055555556 x = -0.509932215 + -0.3055555556 Combine like terms: -0.509932215 + -0.3055555556 = -0.8154877706 x = -0.8154877706 Simplifying x = -0.8154877706Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2043766594, -0.8154877706}
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