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Simplifying x2 + 0.703x + -0.130758 = 0 Reorder the terms: -0.130758 + 0.703x + x2 = 0 Solving -0.130758 + 0.703x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.130758' to each side of the equation. -0.130758 + 0.703x + 0.130758 + x2 = 0 + 0.130758 Reorder the terms: -0.130758 + 0.130758 + 0.703x + x2 = 0 + 0.130758 Combine like terms: -0.130758 + 0.130758 = 0.000000 0.000000 + 0.703x + x2 = 0 + 0.130758 0.703x + x2 = 0 + 0.130758 Combine like terms: 0 + 0.130758 = 0.130758 0.703x + x2 = 0.130758 The x term is 0.703x. Take half its coefficient (0.3515). Square it (0.12355225) and add it to both sides. Add '0.12355225' to each side of the equation. 0.703x + 0.12355225 + x2 = 0.130758 + 0.12355225 Reorder the terms: 0.12355225 + 0.703x + x2 = 0.130758 + 0.12355225 Combine like terms: 0.130758 + 0.12355225 = 0.25431025 0.12355225 + 0.703x + x2 = 0.25431025 Factor a perfect square on the left side: (x + 0.3515)(x + 0.3515) = 0.25431025 Calculate the square root of the right side: 0.50429183 Break this problem into two subproblems by setting (x + 0.3515) equal to 0.50429183 and -0.50429183.Subproblem 1
x + 0.3515 = 0.50429183 Simplifying x + 0.3515 = 0.50429183 Reorder the terms: 0.3515 + x = 0.50429183 Solving 0.3515 + x = 0.50429183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3515' to each side of the equation. 0.3515 + -0.3515 + x = 0.50429183 + -0.3515 Combine like terms: 0.3515 + -0.3515 = 0.0000 0.0000 + x = 0.50429183 + -0.3515 x = 0.50429183 + -0.3515 Combine like terms: 0.50429183 + -0.3515 = 0.15279183 x = 0.15279183 Simplifying x = 0.15279183Subproblem 2
x + 0.3515 = -0.50429183 Simplifying x + 0.3515 = -0.50429183 Reorder the terms: 0.3515 + x = -0.50429183 Solving 0.3515 + x = -0.50429183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3515' to each side of the equation. 0.3515 + -0.3515 + x = -0.50429183 + -0.3515 Combine like terms: 0.3515 + -0.3515 = 0.0000 0.0000 + x = -0.50429183 + -0.3515 x = -0.50429183 + -0.3515 Combine like terms: -0.50429183 + -0.3515 = -0.85579183 x = -0.85579183 Simplifying x = -0.85579183Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15279183, -0.85579183}
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