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Simplifying 4.905x2 + -23x + -6 = 0 Reorder the terms: -6 + -23x + 4.905x2 = 0 Solving -6 + -23x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -1.22324159 + -4.689092762x + x2 = 0 Move the constant term to the right: Add '1.22324159' to each side of the equation. -1.22324159 + -4.689092762x + 1.22324159 + x2 = 0 + 1.22324159 Reorder the terms: -1.22324159 + 1.22324159 + -4.689092762x + x2 = 0 + 1.22324159 Combine like terms: -1.22324159 + 1.22324159 = 0.00000000 0.00000000 + -4.689092762x + x2 = 0 + 1.22324159 -4.689092762x + x2 = 0 + 1.22324159 Combine like terms: 0 + 1.22324159 = 1.22324159 -4.689092762x + x2 = 1.22324159 The x term is -4.689092762x. Take half its coefficient (-2.344546381). Square it (5.496897733) and add it to both sides. Add '5.496897733' to each side of the equation. -4.689092762x + 5.496897733 + x2 = 1.22324159 + 5.496897733 Reorder the terms: 5.496897733 + -4.689092762x + x2 = 1.22324159 + 5.496897733 Combine like terms: 1.22324159 + 5.496897733 = 6.720139323 5.496897733 + -4.689092762x + x2 = 6.720139323 Factor a perfect square on the left side: (x + -2.344546381)(x + -2.344546381) = 6.720139323 Calculate the square root of the right side: 2.592323152 Break this problem into two subproblems by setting (x + -2.344546381) equal to 2.592323152 and -2.592323152.Subproblem 1
x + -2.344546381 = 2.592323152 Simplifying x + -2.344546381 = 2.592323152 Reorder the terms: -2.344546381 + x = 2.592323152 Solving -2.344546381 + x = 2.592323152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.344546381' to each side of the equation. -2.344546381 + 2.344546381 + x = 2.592323152 + 2.344546381 Combine like terms: -2.344546381 + 2.344546381 = 0.000000000 0.000000000 + x = 2.592323152 + 2.344546381 x = 2.592323152 + 2.344546381 Combine like terms: 2.592323152 + 2.344546381 = 4.936869533 x = 4.936869533 Simplifying x = 4.936869533Subproblem 2
x + -2.344546381 = -2.592323152 Simplifying x + -2.344546381 = -2.592323152 Reorder the terms: -2.344546381 + x = -2.592323152 Solving -2.344546381 + x = -2.592323152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.344546381' to each side of the equation. -2.344546381 + 2.344546381 + x = -2.592323152 + 2.344546381 Combine like terms: -2.344546381 + 2.344546381 = 0.000000000 0.000000000 + x = -2.592323152 + 2.344546381 x = -2.592323152 + 2.344546381 Combine like terms: -2.592323152 + 2.344546381 = -0.247776771 x = -0.247776771 Simplifying x = -0.247776771Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.936869533, -0.247776771}
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