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Simplifying 2x2 + -11x + 16 = x2 + 12x + 36 Reorder the terms: 16 + -11x + 2x2 = x2 + 12x + 36 Reorder the terms: 16 + -11x + 2x2 = 36 + 12x + x2 Solving 16 + -11x + 2x2 = 36 + 12x + x2 Solving for variable 'x'. Reorder the terms: 16 + -36 + -11x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 16 + -36 = -20 -20 + -11x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: -11x + -12x = -23x -20 + -23x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -20 + -23x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: -20 + -23x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -20 + -23x + 1x2 = 0 + 12x + -12x + x2 + -1x2 -20 + -23x + 1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -20 + -23x + 1x2 = 0 + x2 + -1x2 -20 + -23x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + -23x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -23x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -23x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -23x + x2 = 0 + 20 -23x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -23x + x2 = 20 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 20 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 20 + 132.25 Combine like terms: 20 + 132.25 = 152.25 132.25 + -23x + x2 = 152.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + -11.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + -11.5 = 12.338962679 Simplifying x + -11.5 = 12.338962679 Reorder the terms: -11.5 + x = 12.338962679 Solving -11.5 + x = 12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 12.338962679 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 12.338962679 + 11.5 x = 12.338962679 + 11.5 Combine like terms: 12.338962679 + 11.5 = 23.838962679 x = 23.838962679 Simplifying x = 23.838962679Subproblem 2
x + -11.5 = -12.338962679 Simplifying x + -11.5 = -12.338962679 Reorder the terms: -11.5 + x = -12.338962679 Solving -11.5 + x = -12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -12.338962679 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -12.338962679 + 11.5 x = -12.338962679 + 11.5 Combine like terms: -12.338962679 + 11.5 = -0.838962679 x = -0.838962679 Simplifying x = -0.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.838962679, -0.838962679}
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