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Simplifying x2 + -23x + 16 = 6x + -4 Reorder the terms: 16 + -23x + x2 = 6x + -4 Reorder the terms: 16 + -23x + x2 = -4 + 6x Solving 16 + -23x + x2 = -4 + 6x Solving for variable 'x'. Reorder the terms: 16 + 4 + -23x + -6x + x2 = -4 + 6x + 4 + -6x Combine like terms: 16 + 4 = 20 20 + -23x + -6x + x2 = -4 + 6x + 4 + -6x Combine like terms: -23x + -6x = -29x 20 + -29x + x2 = -4 + 6x + 4 + -6x Reorder the terms: 20 + -29x + x2 = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 20 + -29x + x2 = 0 + 6x + -6x 20 + -29x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 20 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -29x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -29x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -29x + x2 = 0 + -20 -29x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -29x + x2 = -20 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -20 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -20 + 210.25 Combine like terms: -20 + 210.25 = 190.25 210.25 + -29x + x2 = 190.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + -14.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + -14.5 = 13.793114224 Simplifying x + -14.5 = 13.793114224 Reorder the terms: -14.5 + x = 13.793114224 Solving -14.5 + x = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.793114224 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.793114224 + 14.5 x = 13.793114224 + 14.5 Combine like terms: 13.793114224 + 14.5 = 28.293114224 x = 28.293114224 Simplifying x = 28.293114224Subproblem 2
x + -14.5 = -13.793114224 Simplifying x + -14.5 = -13.793114224 Reorder the terms: -14.5 + x = -13.793114224 Solving -14.5 + x = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.793114224 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.793114224 + 14.5 x = -13.793114224 + 14.5 Combine like terms: -13.793114224 + 14.5 = 0.706885776 x = 0.706885776 Simplifying x = 0.706885776Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.293114224, 0.706885776}
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