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Simplifying 41.9x2 + -45.9x + 11.48 = 0 Reorder the terms: 11.48 + -45.9x + 41.9x2 = 0 Solving 11.48 + -45.9x + 41.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41.9 the coefficient of the squared term: Divide each side by '41.9'. 0.2739856802 + -1.095465394x + x2 = 0 Move the constant term to the right: Add '-0.2739856802' to each side of the equation. 0.2739856802 + -1.095465394x + -0.2739856802 + x2 = 0 + -0.2739856802 Reorder the terms: 0.2739856802 + -0.2739856802 + -1.095465394x + x2 = 0 + -0.2739856802 Combine like terms: 0.2739856802 + -0.2739856802 = 0.0000000000 0.0000000000 + -1.095465394x + x2 = 0 + -0.2739856802 -1.095465394x + x2 = 0 + -0.2739856802 Combine like terms: 0 + -0.2739856802 = -0.2739856802 -1.095465394x + x2 = -0.2739856802 The x term is -1.095465394x. Take half its coefficient (-0.547732697). Square it (0.3000111074) and add it to both sides. Add '0.3000111074' to each side of the equation. -1.095465394x + 0.3000111074 + x2 = -0.2739856802 + 0.3000111074 Reorder the terms: 0.3000111074 + -1.095465394x + x2 = -0.2739856802 + 0.3000111074 Combine like terms: -0.2739856802 + 0.3000111074 = 0.0260254272 0.3000111074 + -1.095465394x + x2 = 0.0260254272 Factor a perfect square on the left side: (x + -0.547732697)(x + -0.547732697) = 0.0260254272 Calculate the square root of the right side: 0.161323982 Break this problem into two subproblems by setting (x + -0.547732697) equal to 0.161323982 and -0.161323982.Subproblem 1
x + -0.547732697 = 0.161323982 Simplifying x + -0.547732697 = 0.161323982 Reorder the terms: -0.547732697 + x = 0.161323982 Solving -0.547732697 + x = 0.161323982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.547732697' to each side of the equation. -0.547732697 + 0.547732697 + x = 0.161323982 + 0.547732697 Combine like terms: -0.547732697 + 0.547732697 = 0.000000000 0.000000000 + x = 0.161323982 + 0.547732697 x = 0.161323982 + 0.547732697 Combine like terms: 0.161323982 + 0.547732697 = 0.709056679 x = 0.709056679 Simplifying x = 0.709056679Subproblem 2
x + -0.547732697 = -0.161323982 Simplifying x + -0.547732697 = -0.161323982 Reorder the terms: -0.547732697 + x = -0.161323982 Solving -0.547732697 + x = -0.161323982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.547732697' to each side of the equation. -0.547732697 + 0.547732697 + x = -0.161323982 + 0.547732697 Combine like terms: -0.547732697 + 0.547732697 = 0.000000000 0.000000000 + x = -0.161323982 + 0.547732697 x = -0.161323982 + 0.547732697 Combine like terms: -0.161323982 + 0.547732697 = 0.386408715 x = 0.386408715 Simplifying x = 0.386408715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.709056679, 0.386408715}
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