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Simplifying 18x2 + 35x + -4 = 0 Reorder the terms: -4 + 35x + 18x2 = 0 Solving -4 + 35x + 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'. -0.2222222222 + 1.944444444x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.944444444x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.944444444x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.944444444x + x2 = 0 + 0.2222222222 1.944444444x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.944444444x + x2 = 0.2222222222 The x term is 1.944444444x. Take half its coefficient (0.972222222). Square it (0.9452160490) and add it to both sides. Add '0.9452160490' to each side of the equation. 1.944444444x + 0.9452160490 + x2 = 0.2222222222 + 0.9452160490 Reorder the terms: 0.9452160490 + 1.944444444x + x2 = 0.2222222222 + 0.9452160490 Combine like terms: 0.2222222222 + 0.9452160490 = 1.1674382712 0.9452160490 + 1.944444444x + x2 = 1.1674382712 Factor a perfect square on the left side: (x + 0.972222222)(x + 0.972222222) = 1.1674382712 Calculate the square root of the right side: 1.080480574 Break this problem into two subproblems by setting (x + 0.972222222) equal to 1.080480574 and -1.080480574.Subproblem 1
x + 0.972222222 = 1.080480574 Simplifying x + 0.972222222 = 1.080480574 Reorder the terms: 0.972222222 + x = 1.080480574 Solving 0.972222222 + x = 1.080480574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.972222222' to each side of the equation. 0.972222222 + -0.972222222 + x = 1.080480574 + -0.972222222 Combine like terms: 0.972222222 + -0.972222222 = 0.000000000 0.000000000 + x = 1.080480574 + -0.972222222 x = 1.080480574 + -0.972222222 Combine like terms: 1.080480574 + -0.972222222 = 0.108258352 x = 0.108258352 Simplifying x = 0.108258352Subproblem 2
x + 0.972222222 = -1.080480574 Simplifying x + 0.972222222 = -1.080480574 Reorder the terms: 0.972222222 + x = -1.080480574 Solving 0.972222222 + x = -1.080480574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.972222222' to each side of the equation. 0.972222222 + -0.972222222 + x = -1.080480574 + -0.972222222 Combine like terms: 0.972222222 + -0.972222222 = 0.000000000 0.000000000 + x = -1.080480574 + -0.972222222 x = -1.080480574 + -0.972222222 Combine like terms: -1.080480574 + -0.972222222 = -2.052702796 x = -2.052702796 Simplifying x = -2.052702796Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.108258352, -2.052702796}
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