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Simplifying 7.67x2 + 2.78x + -5.35 = 0 Reorder the terms: -5.35 + 2.78x + 7.67x2 = 0 Solving -5.35 + 2.78x + 7.67x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.67 the coefficient of the squared term: Divide each side by '7.67'. -0.6975228162 + 0.3624511082x + x2 = 0 Move the constant term to the right: Add '0.6975228162' to each side of the equation. -0.6975228162 + 0.3624511082x + 0.6975228162 + x2 = 0 + 0.6975228162 Reorder the terms: -0.6975228162 + 0.6975228162 + 0.3624511082x + x2 = 0 + 0.6975228162 Combine like terms: -0.6975228162 + 0.6975228162 = 0.0000000000 0.0000000000 + 0.3624511082x + x2 = 0 + 0.6975228162 0.3624511082x + x2 = 0 + 0.6975228162 Combine like terms: 0 + 0.6975228162 = 0.6975228162 0.3624511082x + x2 = 0.6975228162 The x term is 0.3624511082x. Take half its coefficient (0.1812255541). Square it (0.03284270146) and add it to both sides. Add '0.03284270146' to each side of the equation. 0.3624511082x + 0.03284270146 + x2 = 0.6975228162 + 0.03284270146 Reorder the terms: 0.03284270146 + 0.3624511082x + x2 = 0.6975228162 + 0.03284270146 Combine like terms: 0.6975228162 + 0.03284270146 = 0.73036551766 0.03284270146 + 0.3624511082x + x2 = 0.73036551766 Factor a perfect square on the left side: (x + 0.1812255541)(x + 0.1812255541) = 0.73036551766 Calculate the square root of the right side: 0.854614251 Break this problem into two subproblems by setting (x + 0.1812255541) equal to 0.854614251 and -0.854614251.Subproblem 1
x + 0.1812255541 = 0.854614251 Simplifying x + 0.1812255541 = 0.854614251 Reorder the terms: 0.1812255541 + x = 0.854614251 Solving 0.1812255541 + x = 0.854614251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1812255541' to each side of the equation. 0.1812255541 + -0.1812255541 + x = 0.854614251 + -0.1812255541 Combine like terms: 0.1812255541 + -0.1812255541 = 0.0000000000 0.0000000000 + x = 0.854614251 + -0.1812255541 x = 0.854614251 + -0.1812255541 Combine like terms: 0.854614251 + -0.1812255541 = 0.6733886969 x = 0.6733886969 Simplifying x = 0.6733886969Subproblem 2
x + 0.1812255541 = -0.854614251 Simplifying x + 0.1812255541 = -0.854614251 Reorder the terms: 0.1812255541 + x = -0.854614251 Solving 0.1812255541 + x = -0.854614251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1812255541' to each side of the equation. 0.1812255541 + -0.1812255541 + x = -0.854614251 + -0.1812255541 Combine like terms: 0.1812255541 + -0.1812255541 = 0.0000000000 0.0000000000 + x = -0.854614251 + -0.1812255541 x = -0.854614251 + -0.1812255541 Combine like terms: -0.854614251 + -0.1812255541 = -1.0358398051 x = -1.0358398051 Simplifying x = -1.0358398051Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6733886969, -1.0358398051}
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