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Simplifying 3844x2 + 5441x + -80353 = 0 Reorder the terms: -80353 + 5441x + 3844x2 = 0 Solving -80353 + 5441x + 3844x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3844 the coefficient of the squared term: Divide each side by '3844'. -20.90348595 + 1.415452653x + x2 = 0 Move the constant term to the right: Add '20.90348595' to each side of the equation. -20.90348595 + 1.415452653x + 20.90348595 + x2 = 0 + 20.90348595 Reorder the terms: -20.90348595 + 20.90348595 + 1.415452653x + x2 = 0 + 20.90348595 Combine like terms: -20.90348595 + 20.90348595 = 0.00000000 0.00000000 + 1.415452653x + x2 = 0 + 20.90348595 1.415452653x + x2 = 0 + 20.90348595 Combine like terms: 0 + 20.90348595 = 20.90348595 1.415452653x + x2 = 20.90348595 The x term is 1.415452653x. Take half its coefficient (0.7077263265). Square it (0.5008765532) and add it to both sides. Add '0.5008765532' to each side of the equation. 1.415452653x + 0.5008765532 + x2 = 20.90348595 + 0.5008765532 Reorder the terms: 0.5008765532 + 1.415452653x + x2 = 20.90348595 + 0.5008765532 Combine like terms: 20.90348595 + 0.5008765532 = 21.4043625032 0.5008765532 + 1.415452653x + x2 = 21.4043625032 Factor a perfect square on the left side: (x + 0.7077263265)(x + 0.7077263265) = 21.4043625032 Calculate the square root of the right side: 4.626484897 Break this problem into two subproblems by setting (x + 0.7077263265) equal to 4.626484897 and -4.626484897.Subproblem 1
x + 0.7077263265 = 4.626484897 Simplifying x + 0.7077263265 = 4.626484897 Reorder the terms: 0.7077263265 + x = 4.626484897 Solving 0.7077263265 + x = 4.626484897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7077263265' to each side of the equation. 0.7077263265 + -0.7077263265 + x = 4.626484897 + -0.7077263265 Combine like terms: 0.7077263265 + -0.7077263265 = 0.0000000000 0.0000000000 + x = 4.626484897 + -0.7077263265 x = 4.626484897 + -0.7077263265 Combine like terms: 4.626484897 + -0.7077263265 = 3.9187585705 x = 3.9187585705 Simplifying x = 3.9187585705Subproblem 2
x + 0.7077263265 = -4.626484897 Simplifying x + 0.7077263265 = -4.626484897 Reorder the terms: 0.7077263265 + x = -4.626484897 Solving 0.7077263265 + x = -4.626484897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7077263265' to each side of the equation. 0.7077263265 + -0.7077263265 + x = -4.626484897 + -0.7077263265 Combine like terms: 0.7077263265 + -0.7077263265 = 0.0000000000 0.0000000000 + x = -4.626484897 + -0.7077263265 x = -4.626484897 + -0.7077263265 Combine like terms: -4.626484897 + -0.7077263265 = -5.3342112235 x = -5.3342112235 Simplifying x = -5.3342112235Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9187585705, -5.3342112235}
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