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Simplifying 10000x2 + 1.2x + -0.3 = 0 Reorder the terms: -0.3 + 1.2x + 10000x2 = 0 Solving -0.3 + 1.2x + 10000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10000 the coefficient of the squared term: Divide each side by '10000'. -0.00003 + 0.00012x + x2 = 0 Move the constant term to the right: Add '0.00003' to each side of the equation. -0.00003 + 0.00012x + 0.00003 + x2 = 0 + 0.00003 Reorder the terms: -0.00003 + 0.00003 + 0.00012x + x2 = 0 + 0.00003 Combine like terms: -0.00003 + 0.00003 = 0.00000 0.00000 + 0.00012x + x2 = 0 + 0.00003 0.00012x + x2 = 0 + 0.00003 Combine like terms: 0 + 0.00003 = 0.00003 0.00012x + x2 = 0.00003 The x term is 0.00012x. Take half its coefficient (0.00006). Square it (0.0000000036) and add it to both sides. Add '0.0000000036' to each side of the equation. 0.00012x + 0.0000000036 + x2 = 0.00003 + 0.0000000036 Reorder the terms: 0.0000000036 + 0.00012x + x2 = 0.00003 + 0.0000000036 Combine like terms: 0.00003 + 0.0000000036 = 0.0000300036 0.0000000036 + 0.00012x + x2 = 0.0000300036 Factor a perfect square on the left side: (x + 0.00006)(x + 0.00006) = 0.0000300036 Calculate the square root of the right side: 0.005477554 Break this problem into two subproblems by setting (x + 0.00006) equal to 0.005477554 and -0.005477554.Subproblem 1
x + 0.00006 = 0.005477554 Simplifying x + 0.00006 = 0.005477554 Reorder the terms: 0.00006 + x = 0.005477554 Solving 0.00006 + x = 0.005477554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00006' to each side of the equation. 0.00006 + -0.00006 + x = 0.005477554 + -0.00006 Combine like terms: 0.00006 + -0.00006 = 0.00000 0.00000 + x = 0.005477554 + -0.00006 x = 0.005477554 + -0.00006 Combine like terms: 0.005477554 + -0.00006 = 0.005417554 x = 0.005417554 Simplifying x = 0.005417554Subproblem 2
x + 0.00006 = -0.005477554 Simplifying x + 0.00006 = -0.005477554 Reorder the terms: 0.00006 + x = -0.005477554 Solving 0.00006 + x = -0.005477554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00006' to each side of the equation. 0.00006 + -0.00006 + x = -0.005477554 + -0.00006 Combine like terms: 0.00006 + -0.00006 = 0.00000 0.00000 + x = -0.005477554 + -0.00006 x = -0.005477554 + -0.00006 Combine like terms: -0.005477554 + -0.00006 = -0.005537554 x = -0.005537554 Simplifying x = -0.005537554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005417554, -0.005537554}
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