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Simplifying 4.88x2 + -17.14x + 1.776 = 0 Reorder the terms: 1.776 + -17.14x + 4.88x2 = 0 Solving 1.776 + -17.14x + 4.88x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.88 the coefficient of the squared term: Divide each side by '4.88'. 0.3639344262 + -3.512295082x + x2 = 0 Move the constant term to the right: Add '-0.3639344262' to each side of the equation. 0.3639344262 + -3.512295082x + -0.3639344262 + x2 = 0 + -0.3639344262 Reorder the terms: 0.3639344262 + -0.3639344262 + -3.512295082x + x2 = 0 + -0.3639344262 Combine like terms: 0.3639344262 + -0.3639344262 = 0.0000000000 0.0000000000 + -3.512295082x + x2 = 0 + -0.3639344262 -3.512295082x + x2 = 0 + -0.3639344262 Combine like terms: 0 + -0.3639344262 = -0.3639344262 -3.512295082x + x2 = -0.3639344262 The x term is -3.512295082x. Take half its coefficient (-1.756147541). Square it (3.084054186) and add it to both sides. Add '3.084054186' to each side of the equation. -3.512295082x + 3.084054186 + x2 = -0.3639344262 + 3.084054186 Reorder the terms: 3.084054186 + -3.512295082x + x2 = -0.3639344262 + 3.084054186 Combine like terms: -0.3639344262 + 3.084054186 = 2.7201197598 3.084054186 + -3.512295082x + x2 = 2.7201197598 Factor a perfect square on the left side: (x + -1.756147541)(x + -1.756147541) = 2.7201197598 Calculate the square root of the right side: 1.649278557 Break this problem into two subproblems by setting (x + -1.756147541) equal to 1.649278557 and -1.649278557.Subproblem 1
x + -1.756147541 = 1.649278557 Simplifying x + -1.756147541 = 1.649278557 Reorder the terms: -1.756147541 + x = 1.649278557 Solving -1.756147541 + x = 1.649278557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.756147541' to each side of the equation. -1.756147541 + 1.756147541 + x = 1.649278557 + 1.756147541 Combine like terms: -1.756147541 + 1.756147541 = 0.000000000 0.000000000 + x = 1.649278557 + 1.756147541 x = 1.649278557 + 1.756147541 Combine like terms: 1.649278557 + 1.756147541 = 3.405426098 x = 3.405426098 Simplifying x = 3.405426098Subproblem 2
x + -1.756147541 = -1.649278557 Simplifying x + -1.756147541 = -1.649278557 Reorder the terms: -1.756147541 + x = -1.649278557 Solving -1.756147541 + x = -1.649278557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.756147541' to each side of the equation. -1.756147541 + 1.756147541 + x = -1.649278557 + 1.756147541 Combine like terms: -1.756147541 + 1.756147541 = 0.000000000 0.000000000 + x = -1.649278557 + 1.756147541 x = -1.649278557 + 1.756147541 Combine like terms: -1.649278557 + 1.756147541 = 0.106868984 x = 0.106868984 Simplifying x = 0.106868984Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.405426098, 0.106868984}
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