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Simplifying -0.009x2 + 0.265x + -0.951 = 0 Reorder the terms: -0.951 + 0.265x + -0.009x2 = 0 Solving -0.951 + 0.265x + -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'. 105.6666667 + -29.44444444x + x2 = 0 Move the constant term to the right: Add '-105.6666667' to each side of the equation. 105.6666667 + -29.44444444x + -105.6666667 + x2 = 0 + -105.6666667 Reorder the terms: 105.6666667 + -105.6666667 + -29.44444444x + x2 = 0 + -105.6666667 Combine like terms: 105.6666667 + -105.6666667 = 0.0000000 0.0000000 + -29.44444444x + x2 = 0 + -105.6666667 -29.44444444x + x2 = 0 + -105.6666667 Combine like terms: 0 + -105.6666667 = -105.6666667 -29.44444444x + x2 = -105.6666667 The x term is -29.44444444x. Take half its coefficient (-14.72222222). Square it (216.7438271) and add it to both sides. Add '216.7438271' to each side of the equation. -29.44444444x + 216.7438271 + x2 = -105.6666667 + 216.7438271 Reorder the terms: 216.7438271 + -29.44444444x + x2 = -105.6666667 + 216.7438271 Combine like terms: -105.6666667 + 216.7438271 = 111.0771604 216.7438271 + -29.44444444x + x2 = 111.0771604 Factor a perfect square on the left side: (x + -14.72222222)(x + -14.72222222) = 111.0771604 Calculate the square root of the right side: 10.539314987 Break this problem into two subproblems by setting (x + -14.72222222) equal to 10.539314987 and -10.539314987.Subproblem 1
x + -14.72222222 = 10.539314987 Simplifying x + -14.72222222 = 10.539314987 Reorder the terms: -14.72222222 + x = 10.539314987 Solving -14.72222222 + x = 10.539314987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72222222' to each side of the equation. -14.72222222 + 14.72222222 + x = 10.539314987 + 14.72222222 Combine like terms: -14.72222222 + 14.72222222 = 0.00000000 0.00000000 + x = 10.539314987 + 14.72222222 x = 10.539314987 + 14.72222222 Combine like terms: 10.539314987 + 14.72222222 = 25.261537207 x = 25.261537207 Simplifying x = 25.261537207Subproblem 2
x + -14.72222222 = -10.539314987 Simplifying x + -14.72222222 = -10.539314987 Reorder the terms: -14.72222222 + x = -10.539314987 Solving -14.72222222 + x = -10.539314987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72222222' to each side of the equation. -14.72222222 + 14.72222222 + x = -10.539314987 + 14.72222222 Combine like terms: -14.72222222 + 14.72222222 = 0.00000000 0.00000000 + x = -10.539314987 + 14.72222222 x = -10.539314987 + 14.72222222 Combine like terms: -10.539314987 + 14.72222222 = 4.182907233 x = 4.182907233 Simplifying x = 4.182907233Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.261537207, 4.182907233}
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