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Simplifying x2 + -12.3x + -32 = 0 Reorder the terms: -32 + -12.3x + x2 = 0 Solving -32 + -12.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -12.3x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -12.3x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -12.3x + x2 = 0 + 32 -12.3x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -12.3x + x2 = 32 The x term is -12.3x. Take half its coefficient (-6.15). Square it (37.8225) and add it to both sides. Add '37.8225' to each side of the equation. -12.3x + 37.8225 + x2 = 32 + 37.8225 Reorder the terms: 37.8225 + -12.3x + x2 = 32 + 37.8225 Combine like terms: 32 + 37.8225 = 69.8225 37.8225 + -12.3x + x2 = 69.8225 Factor a perfect square on the left side: (x + -6.15)(x + -6.15) = 69.8225 Calculate the square root of the right side: 8.355985878 Break this problem into two subproblems by setting (x + -6.15) equal to 8.355985878 and -8.355985878.Subproblem 1
x + -6.15 = 8.355985878 Simplifying x + -6.15 = 8.355985878 Reorder the terms: -6.15 + x = 8.355985878 Solving -6.15 + x = 8.355985878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.15' to each side of the equation. -6.15 + 6.15 + x = 8.355985878 + 6.15 Combine like terms: -6.15 + 6.15 = 0.00 0.00 + x = 8.355985878 + 6.15 x = 8.355985878 + 6.15 Combine like terms: 8.355985878 + 6.15 = 14.505985878 x = 14.505985878 Simplifying x = 14.505985878Subproblem 2
x + -6.15 = -8.355985878 Simplifying x + -6.15 = -8.355985878 Reorder the terms: -6.15 + x = -8.355985878 Solving -6.15 + x = -8.355985878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.15' to each side of the equation. -6.15 + 6.15 + x = -8.355985878 + 6.15 Combine like terms: -6.15 + 6.15 = 0.00 0.00 + x = -8.355985878 + 6.15 x = -8.355985878 + 6.15 Combine like terms: -8.355985878 + 6.15 = -2.205985878 x = -2.205985878 Simplifying x = -2.205985878Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.505985878, -2.205985878}
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