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Simplifying 23x + x2 = 12 Solving 23x + x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 23x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 23x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 23x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 23x + x2 = 0 + 12 23x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 23x + x2 = 12 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 = 12 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 12 + 132.25 Combine like terms: 12 + 132.25 = 144.25 132.25 + 23x + x2 = 144.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + 11.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + 11.5 = 12.010412149 Simplifying x + 11.5 = 12.010412149 Reorder the terms: 11.5 + x = 12.010412149 Solving 11.5 + x = 12.010412149 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 = 12.010412149 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 12.010412149 + -11.5 x = 12.010412149 + -11.5 Combine like terms: 12.010412149 + -11.5 = 0.510412149 x = 0.510412149 Simplifying x = 0.510412149Subproblem 2
x + 11.5 = -12.010412149 Simplifying x + 11.5 = -12.010412149 Reorder the terms: 11.5 + x = -12.010412149 Solving 11.5 + x = -12.010412149 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 = -12.010412149 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -12.010412149 + -11.5 x = -12.010412149 + -11.5 Combine like terms: -12.010412149 + -11.5 = -23.510412149 x = -23.510412149 Simplifying x = -23.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.510412149, -23.510412149}
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