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Simplifying 7x2 + 3x + -99 = 0 Reorder the terms: -99 + 3x + 7x2 = 0 Solving -99 + 3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -14.14285714 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '14.14285714' to each side of the equation. -14.14285714 + 0.4285714286x + 14.14285714 + x2 = 0 + 14.14285714 Reorder the terms: -14.14285714 + 14.14285714 + 0.4285714286x + x2 = 0 + 14.14285714 Combine like terms: -14.14285714 + 14.14285714 = 0.00000000 0.00000000 + 0.4285714286x + x2 = 0 + 14.14285714 0.4285714286x + x2 = 0 + 14.14285714 Combine like terms: 0 + 14.14285714 = 14.14285714 0.4285714286x + x2 = 14.14285714 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 14.14285714 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 14.14285714 + 0.04591836735 Combine like terms: 14.14285714 + 0.04591836735 = 14.18877550735 0.04591836735 + 0.4285714286x + x2 = 14.18877550735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 14.18877550735 Calculate the square root of the right side: 3.766799106 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 3.766799106 and -3.766799106.Subproblem 1
x + 0.2142857143 = 3.766799106 Simplifying x + 0.2142857143 = 3.766799106 Reorder the terms: 0.2142857143 + x = 3.766799106 Solving 0.2142857143 + x = 3.766799106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 3.766799106 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 3.766799106 + -0.2142857143 x = 3.766799106 + -0.2142857143 Combine like terms: 3.766799106 + -0.2142857143 = 3.5525133917 x = 3.5525133917 Simplifying x = 3.5525133917Subproblem 2
x + 0.2142857143 = -3.766799106 Simplifying x + 0.2142857143 = -3.766799106 Reorder the terms: 0.2142857143 + x = -3.766799106 Solving 0.2142857143 + x = -3.766799106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -3.766799106 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -3.766799106 + -0.2142857143 x = -3.766799106 + -0.2142857143 Combine like terms: -3.766799106 + -0.2142857143 = -3.9810848203 x = -3.9810848203 Simplifying x = -3.9810848203Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5525133917, -3.9810848203}
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