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Simplifying 12x2 + -25x + -42 = 0 Reorder the terms: -42 + -25x + 12x2 = 0 Solving -42 + -25x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.5 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2.083333333x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2.083333333x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2.083333333x + x2 = 0 + 3.5 -2.083333333x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2.083333333x + x2 = 3.5 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = 3.5 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = 3.5 + 1.085069445 Combine like terms: 3.5 + 1.085069445 = 4.585069445 1.085069445 + -2.083333333x + x2 = 4.585069445 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 4.585069445 Calculate the square root of the right side: 2.141277526 Break this problem into two subproblems by setting (x + -1.041666667) equal to 2.141277526 and -2.141277526.Subproblem 1
x + -1.041666667 = 2.141277526 Simplifying x + -1.041666667 = 2.141277526 Reorder the terms: -1.041666667 + x = 2.141277526 Solving -1.041666667 + x = 2.141277526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 2.141277526 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 2.141277526 + 1.041666667 x = 2.141277526 + 1.041666667 Combine like terms: 2.141277526 + 1.041666667 = 3.182944193 x = 3.182944193 Simplifying x = 3.182944193Subproblem 2
x + -1.041666667 = -2.141277526 Simplifying x + -1.041666667 = -2.141277526 Reorder the terms: -1.041666667 + x = -2.141277526 Solving -1.041666667 + x = -2.141277526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -2.141277526 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -2.141277526 + 1.041666667 x = -2.141277526 + 1.041666667 Combine like terms: -2.141277526 + 1.041666667 = -1.099610859 x = -1.099610859 Simplifying x = -1.099610859Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.182944193, -1.099610859}
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