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Simplifying x2 = (6.31 * 0.00001)(0.53 + -1x) Multiply 6.31 * 0.00001 x2 = (0.0000631)(0.53 + -1x) x2 = (0.53 * 0.0000631 + -1x * 0.0000631) x2 = (0.000033443 + -0.0000631x) Solving x2 = 0.000033443 + -0.0000631x Solving for variable 'x'. Reorder the terms: -0.000033443 + 0.0000631x + x2 = 0.000033443 + -0.0000631x + -0.000033443 + 0.0000631x Reorder the terms: -0.000033443 + 0.0000631x + x2 = 0.000033443 + -0.000033443 + -0.0000631x + 0.0000631x Combine like terms: 0.000033443 + -0.000033443 = 0.000000000 -0.000033443 + 0.0000631x + x2 = 0.000000000 + -0.0000631x + 0.0000631x -0.000033443 + 0.0000631x + x2 = -0.0000631x + 0.0000631x Combine like terms: -0.0000631x + 0.0000631x = 0.0000000 -0.000033443 + 0.0000631x + x2 = 0.0000000 Begin completing the square. Move the constant term to the right: Add '0.000033443' to each side of the equation. -0.000033443 + 0.0000631x + 0.000033443 + x2 = 0.0000000 + 0.000033443 Reorder the terms: -0.000033443 + 0.000033443 + 0.0000631x + x2 = 0.0000000 + 0.000033443 Combine like terms: -0.000033443 + 0.000033443 = 0.000000000 0.000000000 + 0.0000631x + x2 = 0.0000000 + 0.000033443 0.0000631x + x2 = 0.0000000 + 0.000033443 Combine like terms: 0.0000000 + 0.000033443 = 0.000033443 0.0000631x + x2 = 0.000033443 The x term is 0.0000631x. Take half its coefficient (0.00003155). Square it (0.0000000009954025) and add it to both sides. Add '0.0000000009954025' to each side of the equation. 0.0000631x + 0.0000000009954025 + x2 = 0.000033443 + 0.0000000009954025 Reorder the terms: 0.0000000009954025 + 0.0000631x + x2 = 0.000033443 + 0.0000000009954025 Combine like terms: 0.000033443 + 0.0000000009954025 = 0.0000334439954025 0.0000000009954025 + 0.0000631x + x2 = 0.0000334439954025 Factor a perfect square on the left side: (x + 0.00003155)(x + 0.00003155) = 0.0000334439954025 Calculate the square root of the right side: 0.005783078 Break this problem into two subproblems by setting (x + 0.00003155) equal to 0.005783078 and -0.005783078.Subproblem 1
x + 0.00003155 = 0.005783078 Simplifying x + 0.00003155 = 0.005783078 Reorder the terms: 0.00003155 + x = 0.005783078 Solving 0.00003155 + x = 0.005783078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00003155' to each side of the equation. 0.00003155 + -0.00003155 + x = 0.005783078 + -0.00003155 Combine like terms: 0.00003155 + -0.00003155 = 0.00000000 0.00000000 + x = 0.005783078 + -0.00003155 x = 0.005783078 + -0.00003155 Combine like terms: 0.005783078 + -0.00003155 = 0.005751528 x = 0.005751528 Simplifying x = 0.005751528Subproblem 2
x + 0.00003155 = -0.005783078 Simplifying x + 0.00003155 = -0.005783078 Reorder the terms: 0.00003155 + x = -0.005783078 Solving 0.00003155 + x = -0.005783078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00003155' to each side of the equation. 0.00003155 + -0.00003155 + x = -0.005783078 + -0.00003155 Combine like terms: 0.00003155 + -0.00003155 = 0.00000000 0.00000000 + x = -0.005783078 + -0.00003155 x = -0.005783078 + -0.00003155 Combine like terms: -0.005783078 + -0.00003155 = -0.005814628 x = -0.005814628 Simplifying x = -0.005814628Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005751528, -0.005814628}
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