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Simplifying 46.3x2 + -150.9x + 100.6 = 0 Reorder the terms: 100.6 + -150.9x + 46.3x2 = 0 Solving 100.6 + -150.9x + 46.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 46.3 the coefficient of the squared term: Divide each side by '46.3'. 2.172786177 + -3.259179266x + x2 = 0 Move the constant term to the right: Add '-2.172786177' to each side of the equation. 2.172786177 + -3.259179266x + -2.172786177 + x2 = 0 + -2.172786177 Reorder the terms: 2.172786177 + -2.172786177 + -3.259179266x + x2 = 0 + -2.172786177 Combine like terms: 2.172786177 + -2.172786177 = 0.000000000 0.000000000 + -3.259179266x + x2 = 0 + -2.172786177 -3.259179266x + x2 = 0 + -2.172786177 Combine like terms: 0 + -2.172786177 = -2.172786177 -3.259179266x + x2 = -2.172786177 The x term is -3.259179266x. Take half its coefficient (-1.629589633). Square it (2.655562372) and add it to both sides. Add '2.655562372' to each side of the equation. -3.259179266x + 2.655562372 + x2 = -2.172786177 + 2.655562372 Reorder the terms: 2.655562372 + -3.259179266x + x2 = -2.172786177 + 2.655562372 Combine like terms: -2.172786177 + 2.655562372 = 0.482776195 2.655562372 + -3.259179266x + x2 = 0.482776195 Factor a perfect square on the left side: (x + -1.629589633)(x + -1.629589633) = 0.482776195 Calculate the square root of the right side: 0.694820981 Break this problem into two subproblems by setting (x + -1.629589633) equal to 0.694820981 and -0.694820981.Subproblem 1
x + -1.629589633 = 0.694820981 Simplifying x + -1.629589633 = 0.694820981 Reorder the terms: -1.629589633 + x = 0.694820981 Solving -1.629589633 + x = 0.694820981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629589633' to each side of the equation. -1.629589633 + 1.629589633 + x = 0.694820981 + 1.629589633 Combine like terms: -1.629589633 + 1.629589633 = 0.000000000 0.000000000 + x = 0.694820981 + 1.629589633 x = 0.694820981 + 1.629589633 Combine like terms: 0.694820981 + 1.629589633 = 2.324410614 x = 2.324410614 Simplifying x = 2.324410614Subproblem 2
x + -1.629589633 = -0.694820981 Simplifying x + -1.629589633 = -0.694820981 Reorder the terms: -1.629589633 + x = -0.694820981 Solving -1.629589633 + x = -0.694820981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629589633' to each side of the equation. -1.629589633 + 1.629589633 + x = -0.694820981 + 1.629589633 Combine like terms: -1.629589633 + 1.629589633 = 0.000000000 0.000000000 + x = -0.694820981 + 1.629589633 x = -0.694820981 + 1.629589633 Combine like terms: -0.694820981 + 1.629589633 = 0.934768652 x = 0.934768652 Simplifying x = 0.934768652Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.324410614, 0.934768652}
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