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Simplifying 18x2 + 7x + -10 = 0 Reorder the terms: -10 + 7x + 18x2 = 0 Solving -10 + 7x + 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 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.3888888889x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.3888888889x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.3888888889x + x2 = 0 + 0.5555555556 0.3888888889x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.3888888889x + x2 = 0.5555555556 The x term is 0.3888888889x. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889x + 0.03780864200 + x2 = 0.5555555556 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = 0.5555555556 + 0.03780864200 Combine like terms: 0.5555555556 + 0.03780864200 = 0.5933641976 0.03780864200 + 0.3888888889x + x2 = 0.5933641976 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = 0.5933641976 Calculate the square root of the right side: 0.770301368 Break this problem into two subproblems by setting (x + 0.1944444445) equal to 0.770301368 and -0.770301368.Subproblem 1
x + 0.1944444445 = 0.770301368 Simplifying x + 0.1944444445 = 0.770301368 Reorder the terms: 0.1944444445 + x = 0.770301368 Solving 0.1944444445 + x = 0.770301368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = 0.770301368 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = 0.770301368 + -0.1944444445 x = 0.770301368 + -0.1944444445 Combine like terms: 0.770301368 + -0.1944444445 = 0.5758569235 x = 0.5758569235 Simplifying x = 0.5758569235Subproblem 2
x + 0.1944444445 = -0.770301368 Simplifying x + 0.1944444445 = -0.770301368 Reorder the terms: 0.1944444445 + x = -0.770301368 Solving 0.1944444445 + x = -0.770301368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = -0.770301368 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = -0.770301368 + -0.1944444445 x = -0.770301368 + -0.1944444445 Combine like terms: -0.770301368 + -0.1944444445 = -0.9647458125 x = -0.9647458125 Simplifying x = -0.9647458125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5758569235, -0.9647458125}
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