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Simplifying 0.009x2 + -0.08x + 0.14 = 0 Reorder the terms: 0.14 + -0.08x + 0.009x2 = 0 Solving 0.14 + -0.08x + 0.009x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.009 the coefficient of the squared term: Divide each side by '0.009'. 15.55555556 + -8.888888889x + x2 = 0 Move the constant term to the right: Add '-15.55555556' to each side of the equation. 15.55555556 + -8.888888889x + -15.55555556 + x2 = 0 + -15.55555556 Reorder the terms: 15.55555556 + -15.55555556 + -8.888888889x + x2 = 0 + -15.55555556 Combine like terms: 15.55555556 + -15.55555556 = 0.00000000 0.00000000 + -8.888888889x + x2 = 0 + -15.55555556 -8.888888889x + x2 = 0 + -15.55555556 Combine like terms: 0 + -15.55555556 = -15.55555556 -8.888888889x + x2 = -15.55555556 The x term is -8.888888889x. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889x + 19.75308642 + x2 = -15.55555556 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889x + x2 = -15.55555556 + 19.75308642 Combine like terms: -15.55555556 + 19.75308642 = 4.19753086 19.75308642 + -8.888888889x + x2 = 4.19753086 Factor a perfect square on the left side: (x + -4.444444445)(x + -4.444444445) = 4.19753086 Calculate the square root of the right side: 2.048787656 Break this problem into two subproblems by setting (x + -4.444444445) equal to 2.048787656 and -2.048787656.Subproblem 1
x + -4.444444445 = 2.048787656 Simplifying x + -4.444444445 = 2.048787656 Reorder the terms: -4.444444445 + x = 2.048787656 Solving -4.444444445 + x = 2.048787656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = 2.048787656 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = 2.048787656 + 4.444444445 x = 2.048787656 + 4.444444445 Combine like terms: 2.048787656 + 4.444444445 = 6.493232101 x = 6.493232101 Simplifying x = 6.493232101Subproblem 2
x + -4.444444445 = -2.048787656 Simplifying x + -4.444444445 = -2.048787656 Reorder the terms: -4.444444445 + x = -2.048787656 Solving -4.444444445 + x = -2.048787656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = -2.048787656 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = -2.048787656 + 4.444444445 x = -2.048787656 + 4.444444445 Combine like terms: -2.048787656 + 4.444444445 = 2.395656789 x = 2.395656789 Simplifying x = 2.395656789Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.493232101, 2.395656789}
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