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Simplifying 12x2 + 25x = 12 Reorder the terms: 25x + 12x2 = 12 Solving 25x + 12x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 25x + 12x2 = 12 + -12 Combine like terms: 12 + -12 = 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 = 0.402310287 x = 0.402310287 Simplifying x = 0.402310287Subproblem 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 = -2.485643621 x = -2.485643621 Simplifying x = -2.485643621Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.402310287, -2.485643621}
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