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Simplifying 45x2 + 14x + -3 = 0 Reorder the terms: -3 + 14x + 45x2 = 0 Solving -3 + 14x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.06666666667 + 0.3111111111x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + 0.3111111111x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + 0.3111111111x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + 0.3111111111x + x2 = 0 + 0.06666666667 0.3111111111x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 0.3111111111x + x2 = 0.06666666667 The x term is 0.3111111111x. Take half its coefficient (0.1555555556). Square it (0.02419753088) and add it to both sides. Add '0.02419753088' to each side of the equation. 0.3111111111x + 0.02419753088 + x2 = 0.06666666667 + 0.02419753088 Reorder the terms: 0.02419753088 + 0.3111111111x + x2 = 0.06666666667 + 0.02419753088 Combine like terms: 0.06666666667 + 0.02419753088 = 0.09086419755 0.02419753088 + 0.3111111111x + x2 = 0.09086419755 Factor a perfect square on the left side: (x + 0.1555555556)(x + 0.1555555556) = 0.09086419755 Calculate the square root of the right side: 0.301436888 Break this problem into two subproblems by setting (x + 0.1555555556) equal to 0.301436888 and -0.301436888.Subproblem 1
x + 0.1555555556 = 0.301436888 Simplifying x + 0.1555555556 = 0.301436888 Reorder the terms: 0.1555555556 + x = 0.301436888 Solving 0.1555555556 + x = 0.301436888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1555555556' to each side of the equation. 0.1555555556 + -0.1555555556 + x = 0.301436888 + -0.1555555556 Combine like terms: 0.1555555556 + -0.1555555556 = 0.0000000000 0.0000000000 + x = 0.301436888 + -0.1555555556 x = 0.301436888 + -0.1555555556 Combine like terms: 0.301436888 + -0.1555555556 = 0.1458813324 x = 0.1458813324 Simplifying x = 0.1458813324Subproblem 2
x + 0.1555555556 = -0.301436888 Simplifying x + 0.1555555556 = -0.301436888 Reorder the terms: 0.1555555556 + x = -0.301436888 Solving 0.1555555556 + x = -0.301436888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1555555556' to each side of the equation. 0.1555555556 + -0.1555555556 + x = -0.301436888 + -0.1555555556 Combine like terms: 0.1555555556 + -0.1555555556 = 0.0000000000 0.0000000000 + x = -0.301436888 + -0.1555555556 x = -0.301436888 + -0.1555555556 Combine like terms: -0.301436888 + -0.1555555556 = -0.4569924436 x = -0.4569924436 Simplifying x = -0.4569924436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1458813324, -0.4569924436}
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