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Simplifying 8.3x2 + 16.2x + -2 = 0 Reorder the terms: -2 + 16.2x + 8.3x2 = 0 Solving -2 + 16.2x + 8.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.3 the coefficient of the squared term: Divide each side by '8.3'. -0.2409638554 + 1.951807229x + x2 = 0 Move the constant term to the right: Add '0.2409638554' to each side of the equation. -0.2409638554 + 1.951807229x + 0.2409638554 + x2 = 0 + 0.2409638554 Reorder the terms: -0.2409638554 + 0.2409638554 + 1.951807229x + x2 = 0 + 0.2409638554 Combine like terms: -0.2409638554 + 0.2409638554 = 0.0000000000 0.0000000000 + 1.951807229x + x2 = 0 + 0.2409638554 1.951807229x + x2 = 0 + 0.2409638554 Combine like terms: 0 + 0.2409638554 = 0.2409638554 1.951807229x + x2 = 0.2409638554 The x term is 1.951807229x. Take half its coefficient (0.9759036145). Square it (0.9523878648) and add it to both sides. Add '0.9523878648' to each side of the equation. 1.951807229x + 0.9523878648 + x2 = 0.2409638554 + 0.9523878648 Reorder the terms: 0.9523878648 + 1.951807229x + x2 = 0.2409638554 + 0.9523878648 Combine like terms: 0.2409638554 + 0.9523878648 = 1.1933517202 0.9523878648 + 1.951807229x + x2 = 1.1933517202 Factor a perfect square on the left side: (x + 0.9759036145)(x + 0.9759036145) = 1.1933517202 Calculate the square root of the right side: 1.09240639 Break this problem into two subproblems by setting (x + 0.9759036145) equal to 1.09240639 and -1.09240639.Subproblem 1
x + 0.9759036145 = 1.09240639 Simplifying x + 0.9759036145 = 1.09240639 Reorder the terms: 0.9759036145 + x = 1.09240639 Solving 0.9759036145 + x = 1.09240639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9759036145' to each side of the equation. 0.9759036145 + -0.9759036145 + x = 1.09240639 + -0.9759036145 Combine like terms: 0.9759036145 + -0.9759036145 = 0.0000000000 0.0000000000 + x = 1.09240639 + -0.9759036145 x = 1.09240639 + -0.9759036145 Combine like terms: 1.09240639 + -0.9759036145 = 0.1165027755 x = 0.1165027755 Simplifying x = 0.1165027755Subproblem 2
x + 0.9759036145 = -1.09240639 Simplifying x + 0.9759036145 = -1.09240639 Reorder the terms: 0.9759036145 + x = -1.09240639 Solving 0.9759036145 + x = -1.09240639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9759036145' to each side of the equation. 0.9759036145 + -0.9759036145 + x = -1.09240639 + -0.9759036145 Combine like terms: 0.9759036145 + -0.9759036145 = 0.0000000000 0.0000000000 + x = -1.09240639 + -0.9759036145 x = -1.09240639 + -0.9759036145 Combine like terms: -1.09240639 + -0.9759036145 = -2.0683100045 x = -2.0683100045 Simplifying x = -2.0683100045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1165027755, -2.0683100045}
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