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Simplifying 12x2 + 12.5x + -5.25 = 0 Reorder the terms: -5.25 + 12.5x + 12x2 = 0 Solving -5.25 + 12.5x + 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'. -0.4375 + 1.041666667x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 1.041666667x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 1.041666667x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 1.041666667x + x2 = 0 + 0.4375 1.041666667x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 1.041666667x + x2 = 0.4375 The x term is 1.041666667x. Take half its coefficient (0.5208333335). Square it (0.2712673613) and add it to both sides. Add '0.2712673613' to each side of the equation. 1.041666667x + 0.2712673613 + x2 = 0.4375 + 0.2712673613 Reorder the terms: 0.2712673613 + 1.041666667x + x2 = 0.4375 + 0.2712673613 Combine like terms: 0.4375 + 0.2712673613 = 0.7087673613 0.2712673613 + 1.041666667x + x2 = 0.7087673613 Factor a perfect square on the left side: (x + 0.5208333335)(x + 0.5208333335) = 0.7087673613 Calculate the square root of the right side: 0.841883223 Break this problem into two subproblems by setting (x + 0.5208333335) equal to 0.841883223 and -0.841883223.Subproblem 1
x + 0.5208333335 = 0.841883223 Simplifying x + 0.5208333335 = 0.841883223 Reorder the terms: 0.5208333335 + x = 0.841883223 Solving 0.5208333335 + x = 0.841883223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = 0.841883223 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = 0.841883223 + -0.5208333335 x = 0.841883223 + -0.5208333335 Combine like terms: 0.841883223 + -0.5208333335 = 0.3210498895 x = 0.3210498895 Simplifying x = 0.3210498895Subproblem 2
x + 0.5208333335 = -0.841883223 Simplifying x + 0.5208333335 = -0.841883223 Reorder the terms: 0.5208333335 + x = -0.841883223 Solving 0.5208333335 + x = -0.841883223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = -0.841883223 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = -0.841883223 + -0.5208333335 x = -0.841883223 + -0.5208333335 Combine like terms: -0.841883223 + -0.5208333335 = -1.3627165565 x = -1.3627165565 Simplifying x = -1.3627165565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3210498895, -1.3627165565}
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