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Simplifying 4.2x2 + -6.3x + 2.3625 = x2 Reorder the terms: 2.3625 + -6.3x + 4.2x2 = x2 Solving 2.3625 + -6.3x + 4.2x2 = x2 Solving for variable 'x'. Combine like terms: 4.2x2 + -1x2 = 3.2x2 2.3625 + -6.3x + 3.2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2.3625 + -6.3x + 3.2x2 = 0 Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 0.73828125 + -1.96875x + x2 = 0 Move the constant term to the right: Add '-0.73828125' to each side of the equation. 0.73828125 + -1.96875x + -0.73828125 + x2 = 0 + -0.73828125 Reorder the terms: 0.73828125 + -0.73828125 + -1.96875x + x2 = 0 + -0.73828125 Combine like terms: 0.73828125 + -0.73828125 = 0.00000000 0.00000000 + -1.96875x + x2 = 0 + -0.73828125 -1.96875x + x2 = 0 + -0.73828125 Combine like terms: 0 + -0.73828125 = -0.73828125 -1.96875x + x2 = -0.73828125 The x term is -1.96875x. Take half its coefficient (-0.984375). Square it (0.9689941406) and add it to both sides. Add '0.9689941406' to each side of the equation. -1.96875x + 0.9689941406 + x2 = -0.73828125 + 0.9689941406 Reorder the terms: 0.9689941406 + -1.96875x + x2 = -0.73828125 + 0.9689941406 Combine like terms: -0.73828125 + 0.9689941406 = 0.2307128906 0.9689941406 + -1.96875x + x2 = 0.2307128906 Factor a perfect square on the left side: (x + -0.984375)(x + -0.984375) = 0.2307128906 Calculate the square root of the right side: 0.480325817 Break this problem into two subproblems by setting (x + -0.984375) equal to 0.480325817 and -0.480325817.Subproblem 1
x + -0.984375 = 0.480325817 Simplifying x + -0.984375 = 0.480325817 Reorder the terms: -0.984375 + x = 0.480325817 Solving -0.984375 + x = 0.480325817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.984375' to each side of the equation. -0.984375 + 0.984375 + x = 0.480325817 + 0.984375 Combine like terms: -0.984375 + 0.984375 = 0.000000 0.000000 + x = 0.480325817 + 0.984375 x = 0.480325817 + 0.984375 Combine like terms: 0.480325817 + 0.984375 = 1.464700817 x = 1.464700817 Simplifying x = 1.464700817Subproblem 2
x + -0.984375 = -0.480325817 Simplifying x + -0.984375 = -0.480325817 Reorder the terms: -0.984375 + x = -0.480325817 Solving -0.984375 + x = -0.480325817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.984375' to each side of the equation. -0.984375 + 0.984375 + x = -0.480325817 + 0.984375 Combine like terms: -0.984375 + 0.984375 = 0.000000 0.000000 + x = -0.480325817 + 0.984375 x = -0.480325817 + 0.984375 Combine like terms: -0.480325817 + 0.984375 = 0.504049183 x = 0.504049183 Simplifying x = 0.504049183Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.464700817, 0.504049183}
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