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Simplifying x2 + 0.853x + -0.087006 = 0 Reorder the terms: -0.087006 + 0.853x + x2 = 0 Solving -0.087006 + 0.853x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.087006' to each side of the equation. -0.087006 + 0.853x + 0.087006 + x2 = 0 + 0.087006 Reorder the terms: -0.087006 + 0.087006 + 0.853x + x2 = 0 + 0.087006 Combine like terms: -0.087006 + 0.087006 = 0.000000 0.000000 + 0.853x + x2 = 0 + 0.087006 0.853x + x2 = 0 + 0.087006 Combine like terms: 0 + 0.087006 = 0.087006 0.853x + x2 = 0.087006 The x term is 0.853x. Take half its coefficient (0.4265). Square it (0.18190225) and add it to both sides. Add '0.18190225' to each side of the equation. 0.853x + 0.18190225 + x2 = 0.087006 + 0.18190225 Reorder the terms: 0.18190225 + 0.853x + x2 = 0.087006 + 0.18190225 Combine like terms: 0.087006 + 0.18190225 = 0.26890825 0.18190225 + 0.853x + x2 = 0.26890825 Factor a perfect square on the left side: (x + 0.4265)(x + 0.4265) = 0.26890825 Calculate the square root of the right side: 0.518563641 Break this problem into two subproblems by setting (x + 0.4265) equal to 0.518563641 and -0.518563641.Subproblem 1
x + 0.4265 = 0.518563641 Simplifying x + 0.4265 = 0.518563641 Reorder the terms: 0.4265 + x = 0.518563641 Solving 0.4265 + x = 0.518563641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4265' to each side of the equation. 0.4265 + -0.4265 + x = 0.518563641 + -0.4265 Combine like terms: 0.4265 + -0.4265 = 0.0000 0.0000 + x = 0.518563641 + -0.4265 x = 0.518563641 + -0.4265 Combine like terms: 0.518563641 + -0.4265 = 0.092063641 x = 0.092063641 Simplifying x = 0.092063641Subproblem 2
x + 0.4265 = -0.518563641 Simplifying x + 0.4265 = -0.518563641 Reorder the terms: 0.4265 + x = -0.518563641 Solving 0.4265 + x = -0.518563641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4265' to each side of the equation. 0.4265 + -0.4265 + x = -0.518563641 + -0.4265 Combine like terms: 0.4265 + -0.4265 = 0.0000 0.0000 + x = -0.518563641 + -0.4265 x = -0.518563641 + -0.4265 Combine like terms: -0.518563641 + -0.4265 = -0.945063641 x = -0.945063641 Simplifying x = -0.945063641Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.092063641, -0.945063641}
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