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Simplifying 23 = 2x2 + -12x + 16 Reorder the terms: 23 = 16 + -12x + 2x2 Solving 23 = 16 + -12x + 2x2 Solving for variable 'x'. Combine like terms: 23 + -16 = 7 7 + 12x + -2x2 = 16 + -12x + 2x2 + -16 + 12x + -2x2 Reorder the terms: 7 + 12x + -2x2 = 16 + -16 + -12x + 12x + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 7 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2 7 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 7 + 12x + -2x2 = 0 + 2x2 + -2x2 7 + 12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -6x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -6x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -6x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -6x + x2 = 0 + 3.5 -6x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -6x + x2 = 3.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 3.5 + 9 Reorder the terms: 9 + -6x + x2 = 3.5 + 9 Combine like terms: 3.5 + 9 = 12.5 9 + -6x + x2 = 12.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -3) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -3 = 3.535533906 Simplifying x + -3 = 3.535533906 Reorder the terms: -3 + x = 3.535533906 Solving -3 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.535533906 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.535533906 + 3 x = 3.535533906 + 3 Combine like terms: 3.535533906 + 3 = 6.535533906 x = 6.535533906 Simplifying x = 6.535533906Subproblem 2
x + -3 = -3.535533906 Simplifying x + -3 = -3.535533906 Reorder the terms: -3 + x = -3.535533906 Solving -3 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.535533906 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.535533906 + 3 x = -3.535533906 + 3 Combine like terms: -3.535533906 + 3 = -0.535533906 x = -0.535533906 Simplifying x = -0.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.535533906, -0.535533906}
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