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Simplifying 829x + 89x2 + 9 = 0 Reorder the terms: 9 + 829x + 89x2 = 0 Solving 9 + 829x + 89x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 89 the coefficient of the squared term: Divide each side by '89'. 0.1011235955 + 9.314606742x + x2 = 0 Move the constant term to the right: Add '-0.1011235955' to each side of the equation. 0.1011235955 + 9.314606742x + -0.1011235955 + x2 = 0 + -0.1011235955 Reorder the terms: 0.1011235955 + -0.1011235955 + 9.314606742x + x2 = 0 + -0.1011235955 Combine like terms: 0.1011235955 + -0.1011235955 = 0.0000000000 0.0000000000 + 9.314606742x + x2 = 0 + -0.1011235955 9.314606742x + x2 = 0 + -0.1011235955 Combine like terms: 0 + -0.1011235955 = -0.1011235955 9.314606742x + x2 = -0.1011235955 The x term is 9.314606742x. Take half its coefficient (4.657303371). Square it (21.69047469) and add it to both sides. Add '21.69047469' to each side of the equation. 9.314606742x + 21.69047469 + x2 = -0.1011235955 + 21.69047469 Reorder the terms: 21.69047469 + 9.314606742x + x2 = -0.1011235955 + 21.69047469 Combine like terms: -0.1011235955 + 21.69047469 = 21.5893510945 21.69047469 + 9.314606742x + x2 = 21.5893510945 Factor a perfect square on the left side: (x + 4.657303371)(x + 4.657303371) = 21.5893510945 Calculate the square root of the right side: 4.646434234 Break this problem into two subproblems by setting (x + 4.657303371) equal to 4.646434234 and -4.646434234.Subproblem 1
x + 4.657303371 = 4.646434234 Simplifying x + 4.657303371 = 4.646434234 Reorder the terms: 4.657303371 + x = 4.646434234 Solving 4.657303371 + x = 4.646434234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.657303371' to each side of the equation. 4.657303371 + -4.657303371 + x = 4.646434234 + -4.657303371 Combine like terms: 4.657303371 + -4.657303371 = 0.000000000 0.000000000 + x = 4.646434234 + -4.657303371 x = 4.646434234 + -4.657303371 Combine like terms: 4.646434234 + -4.657303371 = -0.010869137 x = -0.010869137 Simplifying x = -0.010869137Subproblem 2
x + 4.657303371 = -4.646434234 Simplifying x + 4.657303371 = -4.646434234 Reorder the terms: 4.657303371 + x = -4.646434234 Solving 4.657303371 + x = -4.646434234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.657303371' to each side of the equation. 4.657303371 + -4.657303371 + x = -4.646434234 + -4.657303371 Combine like terms: 4.657303371 + -4.657303371 = 0.000000000 0.000000000 + x = -4.646434234 + -4.657303371 x = -4.646434234 + -4.657303371 Combine like terms: -4.646434234 + -4.657303371 = -9.303737605 x = -9.303737605 Simplifying x = -9.303737605Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.010869137, -9.303737605}
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