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Simplifying 16x2 + 1090x + x + -3.2 = 0 Reorder the terms: -3.2 + 1090x + x + 16x2 = 0 Combine like terms: 1090x + x = 1091x -3.2 + 1091x + 16x2 = 0 Solving -3.2 + 1091x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.2 + 68.1875x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 68.1875x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 68.1875x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 68.1875x + x2 = 0 + 0.2 68.1875x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 68.1875x + x2 = 0.2 The x term is 68.1875x. Take half its coefficient (34.09375). Square it (1162.383789) and add it to both sides. Add '1162.383789' to each side of the equation. 68.1875x + 1162.383789 + x2 = 0.2 + 1162.383789 Reorder the terms: 1162.383789 + 68.1875x + x2 = 0.2 + 1162.383789 Combine like terms: 0.2 + 1162.383789 = 1162.583789 1162.383789 + 68.1875x + x2 = 1162.583789 Factor a perfect square on the left side: (x + 34.09375)(x + 34.09375) = 1162.583789 Calculate the square root of the right side: 34.096682962 Break this problem into two subproblems by setting (x + 34.09375) equal to 34.096682962 and -34.096682962.Subproblem 1
x + 34.09375 = 34.096682962 Simplifying x + 34.09375 = 34.096682962 Reorder the terms: 34.09375 + x = 34.096682962 Solving 34.09375 + x = 34.096682962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.09375' to each side of the equation. 34.09375 + -34.09375 + x = 34.096682962 + -34.09375 Combine like terms: 34.09375 + -34.09375 = 0.00000 0.00000 + x = 34.096682962 + -34.09375 x = 34.096682962 + -34.09375 Combine like terms: 34.096682962 + -34.09375 = 0.002932962 x = 0.002932962 Simplifying x = 0.002932962Subproblem 2
x + 34.09375 = -34.096682962 Simplifying x + 34.09375 = -34.096682962 Reorder the terms: 34.09375 + x = -34.096682962 Solving 34.09375 + x = -34.096682962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.09375' to each side of the equation. 34.09375 + -34.09375 + x = -34.096682962 + -34.09375 Combine like terms: 34.09375 + -34.09375 = 0.00000 0.00000 + x = -34.096682962 + -34.09375 x = -34.096682962 + -34.09375 Combine like terms: -34.096682962 + -34.09375 = -68.190432962 x = -68.190432962 Simplifying x = -68.190432962Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002932962, -68.190432962}
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