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Simplifying 100x + 442212.239x2 = 0.62 Solving 100x + 442212.239x2 = 0.62 Solving for variable 'x'. Reorder the terms: -0.62 + 100x + 442212.239x2 = 0.62 + -0.62 Combine like terms: 0.62 + -0.62 = 0.00 -0.62 + 100x + 442212.239x2 = 0.00 Begin completing the square. Divide all terms by 442212.239 the coefficient of the squared term: Divide each side by '442212.239'. -0.000001402041702 + 0.0002261357583x + x2 = 0 Move the constant term to the right: Add '0.000001402041702' to each side of the equation. -0.000001402041702 + 0.0002261357583x + 0.000001402041702 + x2 = 0 + 0.000001402041702 Reorder the terms: -0.000001402041702 + 0.000001402041702 + 0.0002261357583x + x2 = 0 + 0.000001402041702 Combine like terms: -0.000001402041702 + 0.000001402041702 = 0.000000000000000 0.000000000000000 + 0.0002261357583x + x2 = 0 + 0.000001402041702 0.0002261357583x + x2 = 0 + 0.000001402041702 Combine like terms: 0 + 0.000001402041702 = 0.000001402041702 0.0002261357583x + x2 = 0.000001402041702 The x term is 0.0002261357583x. Take half its coefficient (0.0001130678792). Square it (0.00000001278434531) and add it to both sides. Add '0.00000001278434531' to each side of the equation. 0.0002261357583x + 0.00000001278434531 + x2 = 0.000001402041702 + 0.00000001278434531 Reorder the terms: 0.00000001278434531 + 0.0002261357583x + x2 = 0.000001402041702 + 0.00000001278434531 Combine like terms: 0.000001402041702 + 0.00000001278434531 = 0.00000141482604731 0.00000001278434531 + 0.0002261357583x + x2 = 0.00000141482604731 Factor a perfect square on the left side: (x + 0.0001130678792)(x + 0.0001130678792) = 0.00000141482604731 Calculate the square root of the right side: 0.001189465 Break this problem into two subproblems by setting (x + 0.0001130678792) equal to 0.001189465 and -0.001189465.Subproblem 1
x + 0.0001130678792 = 0.001189465 Simplifying x + 0.0001130678792 = 0.001189465 Reorder the terms: 0.0001130678792 + x = 0.001189465 Solving 0.0001130678792 + x = 0.001189465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001130678792' to each side of the equation. 0.0001130678792 + -0.0001130678792 + x = 0.001189465 + -0.0001130678792 Combine like terms: 0.0001130678792 + -0.0001130678792 = 0.0000000000000 0.0000000000000 + x = 0.001189465 + -0.0001130678792 x = 0.001189465 + -0.0001130678792 Combine like terms: 0.001189465 + -0.0001130678792 = 0.0010763971208 x = 0.0010763971208 Simplifying x = 0.0010763971208Subproblem 2
x + 0.0001130678792 = -0.001189465 Simplifying x + 0.0001130678792 = -0.001189465 Reorder the terms: 0.0001130678792 + x = -0.001189465 Solving 0.0001130678792 + x = -0.001189465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001130678792' to each side of the equation. 0.0001130678792 + -0.0001130678792 + x = -0.001189465 + -0.0001130678792 Combine like terms: 0.0001130678792 + -0.0001130678792 = 0.0000000000000 0.0000000000000 + x = -0.001189465 + -0.0001130678792 x = -0.001189465 + -0.0001130678792 Combine like terms: -0.001189465 + -0.0001130678792 = -0.0013025328792 x = -0.0013025328792 Simplifying x = -0.0013025328792Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0010763971208, -0.0013025328792}
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