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Simplifying 4x2 + 0.106x + -0.106 = 0 Reorder the terms: -0.106 + 0.106x + 4x2 = 0 Solving -0.106 + 0.106x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.0265 + 0.0265x + x2 = 0 Move the constant term to the right: Add '0.0265' to each side of the equation. -0.0265 + 0.0265x + 0.0265 + x2 = 0 + 0.0265 Reorder the terms: -0.0265 + 0.0265 + 0.0265x + x2 = 0 + 0.0265 Combine like terms: -0.0265 + 0.0265 = 0.0000 0.0000 + 0.0265x + x2 = 0 + 0.0265 0.0265x + x2 = 0 + 0.0265 Combine like terms: 0 + 0.0265 = 0.0265 0.0265x + x2 = 0.0265 The x term is 0.0265x. Take half its coefficient (0.01325). Square it (0.0001755625) and add it to both sides. Add '0.0001755625' to each side of the equation. 0.0265x + 0.0001755625 + x2 = 0.0265 + 0.0001755625 Reorder the terms: 0.0001755625 + 0.0265x + x2 = 0.0265 + 0.0001755625 Combine like terms: 0.0265 + 0.0001755625 = 0.0266755625 0.0001755625 + 0.0265x + x2 = 0.0266755625 Factor a perfect square on the left side: (x + 0.01325)(x + 0.01325) = 0.0266755625 Calculate the square root of the right side: 0.163326552 Break this problem into two subproblems by setting (x + 0.01325) equal to 0.163326552 and -0.163326552.Subproblem 1
x + 0.01325 = 0.163326552 Simplifying x + 0.01325 = 0.163326552 Reorder the terms: 0.01325 + x = 0.163326552 Solving 0.01325 + x = 0.163326552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01325' to each side of the equation. 0.01325 + -0.01325 + x = 0.163326552 + -0.01325 Combine like terms: 0.01325 + -0.01325 = 0.00000 0.00000 + x = 0.163326552 + -0.01325 x = 0.163326552 + -0.01325 Combine like terms: 0.163326552 + -0.01325 = 0.150076552 x = 0.150076552 Simplifying x = 0.150076552Subproblem 2
x + 0.01325 = -0.163326552 Simplifying x + 0.01325 = -0.163326552 Reorder the terms: 0.01325 + x = -0.163326552 Solving 0.01325 + x = -0.163326552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01325' to each side of the equation. 0.01325 + -0.01325 + x = -0.163326552 + -0.01325 Combine like terms: 0.01325 + -0.01325 = 0.00000 0.00000 + x = -0.163326552 + -0.01325 x = -0.163326552 + -0.01325 Combine like terms: -0.163326552 + -0.01325 = -0.176576552 x = -0.176576552 Simplifying x = -0.176576552Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150076552, -0.176576552}
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