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Simplifying (0.000065)(0.10 + -1x) = x2 (0.10 * 0.000065 + -1x * 0.000065) = x2 (0.0000065 + -0.000065x) = x2 Solving 0.0000065 + -0.000065x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.0000065 + -0.000065x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0000065 + 0.000065x + x2 = 0 Move the constant term to the right: Add '0.0000065' to each side of the equation. -0.0000065 + 0.000065x + 0.0000065 + x2 = 0 + 0.0000065 Reorder the terms: -0.0000065 + 0.0000065 + 0.000065x + x2 = 0 + 0.0000065 Combine like terms: -0.0000065 + 0.0000065 = 0.0000000 0.0000000 + 0.000065x + x2 = 0 + 0.0000065 0.000065x + x2 = 0 + 0.0000065 Combine like terms: 0 + 0.0000065 = 0.0000065 0.000065x + x2 = 0.0000065 The x term is 0.000065x. Take half its coefficient (0.0000325). Square it (0.00000000105625) and add it to both sides. Add '0.00000000105625' to each side of the equation. 0.000065x + 0.00000000105625 + x2 = 0.0000065 + 0.00000000105625 Reorder the terms: 0.00000000105625 + 0.000065x + x2 = 0.0000065 + 0.00000000105625 Combine like terms: 0.0000065 + 0.00000000105625 = 0.00000650105625 0.00000000105625 + 0.000065x + x2 = 0.00000650105625 Factor a perfect square on the left side: (x + 0.0000325)(x + 0.0000325) = 0.00000650105625 Calculate the square root of the right side: 0.002549717 Break this problem into two subproblems by setting (x + 0.0000325) equal to 0.002549717 and -0.002549717.Subproblem 1
x + 0.0000325 = 0.002549717 Simplifying x + 0.0000325 = 0.002549717 Reorder the terms: 0.0000325 + x = 0.002549717 Solving 0.0000325 + x = 0.002549717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000325' to each side of the equation. 0.0000325 + -0.0000325 + x = 0.002549717 + -0.0000325 Combine like terms: 0.0000325 + -0.0000325 = 0.0000000 0.0000000 + x = 0.002549717 + -0.0000325 x = 0.002549717 + -0.0000325 Combine like terms: 0.002549717 + -0.0000325 = 0.002517217 x = 0.002517217 Simplifying x = 0.002517217Subproblem 2
x + 0.0000325 = -0.002549717 Simplifying x + 0.0000325 = -0.002549717 Reorder the terms: 0.0000325 + x = -0.002549717 Solving 0.0000325 + x = -0.002549717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000325' to each side of the equation. 0.0000325 + -0.0000325 + x = -0.002549717 + -0.0000325 Combine like terms: 0.0000325 + -0.0000325 = 0.0000000 0.0000000 + x = -0.002549717 + -0.0000325 x = -0.002549717 + -0.0000325 Combine like terms: -0.002549717 + -0.0000325 = -0.002582217 x = -0.002582217 Simplifying x = -0.002582217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002517217, -0.002582217}
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