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Simplifying 2x2 + -7x = 12.25 Reorder the terms: -7x + 2x2 = 12.25 Solving -7x + 2x2 = 12.25 Solving for variable 'x'. Reorder the terms: -12.25 + -7x + 2x2 = 12.25 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 -12.25 + -7x + 2x2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.125 + -3.5x + x2 = 0.00 Move the constant term to the right: Add '6.125' to each side of the equation. -6.125 + -3.5x + 6.125 + x2 = 0.00 + 6.125 Reorder the terms: -6.125 + 6.125 + -3.5x + x2 = 0.00 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + -3.5x + x2 = 0.00 + 6.125 -3.5x + x2 = 0.00 + 6.125 Combine like terms: 0.00 + 6.125 = 6.125 -3.5x + x2 = 6.125 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 6.125 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 6.125 + 3.0625 Combine like terms: 6.125 + 3.0625 = 9.1875 3.0625 + -3.5x + x2 = 9.1875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 9.1875 Calculate the square root of the right side: 3.031088913 Break this problem into two subproblems by setting (x + -1.75) equal to 3.031088913 and -3.031088913.Subproblem 1
x + -1.75 = 3.031088913 Simplifying x + -1.75 = 3.031088913 Reorder the terms: -1.75 + x = 3.031088913 Solving -1.75 + x = 3.031088913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.031088913 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.031088913 + 1.75 x = 3.031088913 + 1.75 Combine like terms: 3.031088913 + 1.75 = 4.781088913 x = 4.781088913 Simplifying x = 4.781088913Subproblem 2
x + -1.75 = -3.031088913 Simplifying x + -1.75 = -3.031088913 Reorder the terms: -1.75 + x = -3.031088913 Solving -1.75 + x = -3.031088913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.031088913 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.031088913 + 1.75 x = -3.031088913 + 1.75 Combine like terms: -3.031088913 + 1.75 = -1.281088913 x = -1.281088913 Simplifying x = -1.281088913Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.781088913, -1.281088913}
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