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Simplifying 10000000x2 + 1.2x + -0.3 = 0 Reorder the terms: -0.3 + 1.2x + 10000000x2 = 0 Solving -0.3 + 1.2x + 10000000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10000000 the coefficient of the squared term: Divide each side by '10000000'. -0.00000003 + 0.00000012x + x2 = 0 Move the constant term to the right: Add '0.00000003' to each side of the equation. -0.00000003 + 0.00000012x + 0.00000003 + x2 = 0 + 0.00000003 Reorder the terms: -0.00000003 + 0.00000003 + 0.00000012x + x2 = 0 + 0.00000003 Combine like terms: -0.00000003 + 0.00000003 = 0.00000000 0.00000000 + 0.00000012x + x2 = 0 + 0.00000003 0.00000012x + x2 = 0 + 0.00000003 Combine like terms: 0 + 0.00000003 = 0.00000003 0.00000012x + x2 = 0.00000003 The x term is 0.00000012x. Take half its coefficient (0.00000006). Square it (0.0000000000000036) and add it to both sides. Add '0.0000000000000036' to each side of the equation. 0.00000012x + 0.0000000000000036 + x2 = 0.00000003 + 0.0000000000000036 Reorder the terms: 0.0000000000000036 + 0.00000012x + x2 = 0.00000003 + 0.0000000000000036 Combine like terms: 0.00000003 + 0.0000000000000036 = 0.0000000300000036 0.0000000000000036 + 0.00000012x + x2 = 0.0000000300000036 Factor a perfect square on the left side: (x + 0.00000006)(x + 0.00000006) = 0.0000000300000036 Calculate the square root of the right side: 0.000173205 Break this problem into two subproblems by setting (x + 0.00000006) equal to 0.000173205 and -0.000173205.Subproblem 1
x + 0.00000006 = 0.000173205 Simplifying x + 0.00000006 = 0.000173205 Reorder the terms: 0.00000006 + x = 0.000173205 Solving 0.00000006 + x = 0.000173205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000006' to each side of the equation. 0.00000006 + -0.00000006 + x = 0.000173205 + -0.00000006 Combine like terms: 0.00000006 + -0.00000006 = 0.00000000 0.00000000 + x = 0.000173205 + -0.00000006 x = 0.000173205 + -0.00000006 Combine like terms: 0.000173205 + -0.00000006 = 0.000173145 x = 0.000173145 Simplifying x = 0.000173145Subproblem 2
x + 0.00000006 = -0.000173205 Simplifying x + 0.00000006 = -0.000173205 Reorder the terms: 0.00000006 + x = -0.000173205 Solving 0.00000006 + x = -0.000173205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000006' to each side of the equation. 0.00000006 + -0.00000006 + x = -0.000173205 + -0.00000006 Combine like terms: 0.00000006 + -0.00000006 = 0.00000000 0.00000000 + x = -0.000173205 + -0.00000006 x = -0.000173205 + -0.00000006 Combine like terms: -0.000173205 + -0.00000006 = -0.000173265 x = -0.000173265 Simplifying x = -0.000173265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000173145, -0.000173265}
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