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Simplifying 28x2 + 29x + -12 = 0 Reorder the terms: -12 + 29x + 28x2 = 0 Solving -12 + 29x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.4285714286 + 1.035714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.035714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.035714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.035714286x + x2 = 0 + 0.4285714286 1.035714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.035714286x + x2 = 0.4285714286 The x term is 1.035714286x. Take half its coefficient (0.517857143). Square it (0.2681760206) and add it to both sides. Add '0.2681760206' to each side of the equation. 1.035714286x + 0.2681760206 + x2 = 0.4285714286 + 0.2681760206 Reorder the terms: 0.2681760206 + 1.035714286x + x2 = 0.4285714286 + 0.2681760206 Combine like terms: 0.4285714286 + 0.2681760206 = 0.6967474492 0.2681760206 + 1.035714286x + x2 = 0.6967474492 Factor a perfect square on the left side: (x + 0.517857143)(x + 0.517857143) = 0.6967474492 Calculate the square root of the right side: 0.834713992 Break this problem into two subproblems by setting (x + 0.517857143) equal to 0.834713992 and -0.834713992.Subproblem 1
x + 0.517857143 = 0.834713992 Simplifying x + 0.517857143 = 0.834713992 Reorder the terms: 0.517857143 + x = 0.834713992 Solving 0.517857143 + x = 0.834713992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.517857143' to each side of the equation. 0.517857143 + -0.517857143 + x = 0.834713992 + -0.517857143 Combine like terms: 0.517857143 + -0.517857143 = 0.000000000 0.000000000 + x = 0.834713992 + -0.517857143 x = 0.834713992 + -0.517857143 Combine like terms: 0.834713992 + -0.517857143 = 0.316856849 x = 0.316856849 Simplifying x = 0.316856849Subproblem 2
x + 0.517857143 = -0.834713992 Simplifying x + 0.517857143 = -0.834713992 Reorder the terms: 0.517857143 + x = -0.834713992 Solving 0.517857143 + x = -0.834713992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.517857143' to each side of the equation. 0.517857143 + -0.517857143 + x = -0.834713992 + -0.517857143 Combine like terms: 0.517857143 + -0.517857143 = 0.000000000 0.000000000 + x = -0.834713992 + -0.517857143 x = -0.834713992 + -0.517857143 Combine like terms: -0.834713992 + -0.517857143 = -1.352571135 x = -1.352571135 Simplifying x = -1.352571135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.316856849, -1.352571135}
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