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Simplifying 0 = 12 + 25x + -12x2 Solving 0 = 12 + 25x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -25x + 12x2 = 12 + 25x + -12x2 + -12 + -25x + 12x2 Reorder the terms: -12 + -25x + 12x2 = 12 + -12 + 25x + -25x + -12x2 + 12x2 Combine like terms: 12 + -12 = 0 -12 + -25x + 12x2 = 0 + 25x + -25x + -12x2 + 12x2 -12 + -25x + 12x2 = 25x + -25x + -12x2 + 12x2 Combine like terms: 25x + -25x = 0 -12 + -25x + 12x2 = 0 + -12x2 + 12x2 -12 + -25x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -12 + -25x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.083333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.083333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.083333333x + x2 = 0 + 1 -2.083333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.083333333x + x2 = 1 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 = 1 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = 1 + 1.085069445 Combine like terms: 1 + 1.085069445 = 2.085069445 1.085069445 + -2.083333333x + x2 = 2.085069445 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 2.085069445 Calculate the square root of the right side: 1.443976954 Break this problem into two subproblems by setting (x + -1.041666667) equal to 1.443976954 and -1.443976954.Subproblem 1
x + -1.041666667 = 1.443976954 Simplifying x + -1.041666667 = 1.443976954 Reorder the terms: -1.041666667 + x = 1.443976954 Solving -1.041666667 + x = 1.443976954 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 = 1.443976954 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 1.443976954 + 1.041666667 x = 1.443976954 + 1.041666667 Combine like terms: 1.443976954 + 1.041666667 = 2.485643621 x = 2.485643621 Simplifying x = 2.485643621Subproblem 2
x + -1.041666667 = -1.443976954 Simplifying x + -1.041666667 = -1.443976954 Reorder the terms: -1.041666667 + x = -1.443976954 Solving -1.041666667 + x = -1.443976954 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 = -1.443976954 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -1.443976954 + 1.041666667 x = -1.443976954 + 1.041666667 Combine like terms: -1.443976954 + 1.041666667 = -0.402310287 x = -0.402310287 Simplifying x = -0.402310287Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.485643621, -0.402310287}
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