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Simplifying 18x2 + -30x + -25 = 0 Reorder the terms: -25 + -30x + 18x2 = 0 Solving -25 + -30x + 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'. -1.388888889 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.388888889' to each side of the equation. -1.388888889 + -1.666666667x + 1.388888889 + x2 = 0 + 1.388888889 Reorder the terms: -1.388888889 + 1.388888889 + -1.666666667x + x2 = 0 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.388888889 -1.666666667x + x2 = 0 + 1.388888889 Combine like terms: 0 + 1.388888889 = 1.388888889 -1.666666667x + x2 = 1.388888889 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1.388888889 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.388888889 + 0.6944444447 Combine like terms: 1.388888889 + 0.6944444447 = 2.0833333337 0.6944444447 + -1.666666667x + x2 = 2.0833333337 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 2.0833333337 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.443375673 and -1.443375673.Subproblem 1
x + -0.8333333335 = 1.443375673 Simplifying x + -0.8333333335 = 1.443375673 Reorder the terms: -0.8333333335 + x = 1.443375673 Solving -0.8333333335 + x = 1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.443375673 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.443375673 + 0.8333333335 x = 1.443375673 + 0.8333333335 Combine like terms: 1.443375673 + 0.8333333335 = 2.2767090065 x = 2.2767090065 Simplifying x = 2.2767090065Subproblem 2
x + -0.8333333335 = -1.443375673 Simplifying x + -0.8333333335 = -1.443375673 Reorder the terms: -0.8333333335 + x = -1.443375673 Solving -0.8333333335 + x = -1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.443375673 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.443375673 + 0.8333333335 x = -1.443375673 + 0.8333333335 Combine like terms: -1.443375673 + 0.8333333335 = -0.6100423395 x = -0.6100423395 Simplifying x = -0.6100423395Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2767090065, -0.6100423395}
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