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Simplifying 29x2 + -32x + -30 = 0 Reorder the terms: -30 + -32x + 29x2 = 0 Solving -30 + -32x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -1.034482759 + -1.103448276x + x2 = 0 Move the constant term to the right: Add '1.034482759' to each side of the equation. -1.034482759 + -1.103448276x + 1.034482759 + x2 = 0 + 1.034482759 Reorder the terms: -1.034482759 + 1.034482759 + -1.103448276x + x2 = 0 + 1.034482759 Combine like terms: -1.034482759 + 1.034482759 = 0.000000000 0.000000000 + -1.103448276x + x2 = 0 + 1.034482759 -1.103448276x + x2 = 0 + 1.034482759 Combine like terms: 0 + 1.034482759 = 1.034482759 -1.103448276x + x2 = 1.034482759 The x term is -1.103448276x. Take half its coefficient (-0.551724138). Square it (0.3043995245) and add it to both sides. Add '0.3043995245' to each side of the equation. -1.103448276x + 0.3043995245 + x2 = 1.034482759 + 0.3043995245 Reorder the terms: 0.3043995245 + -1.103448276x + x2 = 1.034482759 + 0.3043995245 Combine like terms: 1.034482759 + 0.3043995245 = 1.3388822835 0.3043995245 + -1.103448276x + x2 = 1.3388822835 Factor a perfect square on the left side: (x + -0.551724138)(x + -0.551724138) = 1.3388822835 Calculate the square root of the right side: 1.15710081 Break this problem into two subproblems by setting (x + -0.551724138) equal to 1.15710081 and -1.15710081.Subproblem 1
x + -0.551724138 = 1.15710081 Simplifying x + -0.551724138 = 1.15710081 Reorder the terms: -0.551724138 + x = 1.15710081 Solving -0.551724138 + x = 1.15710081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.551724138' to each side of the equation. -0.551724138 + 0.551724138 + x = 1.15710081 + 0.551724138 Combine like terms: -0.551724138 + 0.551724138 = 0.000000000 0.000000000 + x = 1.15710081 + 0.551724138 x = 1.15710081 + 0.551724138 Combine like terms: 1.15710081 + 0.551724138 = 1.708824948 x = 1.708824948 Simplifying x = 1.708824948Subproblem 2
x + -0.551724138 = -1.15710081 Simplifying x + -0.551724138 = -1.15710081 Reorder the terms: -0.551724138 + x = -1.15710081 Solving -0.551724138 + x = -1.15710081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.551724138' to each side of the equation. -0.551724138 + 0.551724138 + x = -1.15710081 + 0.551724138 Combine like terms: -0.551724138 + 0.551724138 = 0.000000000 0.000000000 + x = -1.15710081 + 0.551724138 x = -1.15710081 + 0.551724138 Combine like terms: -1.15710081 + 0.551724138 = -0.605376672 x = -0.605376672 Simplifying x = -0.605376672Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.708824948, -0.605376672}
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