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Simplifying 14x + -4x2 = 12.25 Solving 14x + -4x2 = 12.25 Solving for variable 'x'. Reorder the terms: -12.25 + 14x + -4x2 = 12.25 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 -12.25 + 14x + -4x2 = 0.00 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.0625 + -3.5x + x2 = 0.00 Move the constant term to the right: Add '-3.0625' to each side of the equation. 3.0625 + -3.5x + -3.0625 + x2 = 0.00 + -3.0625 Reorder the terms: 3.0625 + -3.0625 + -3.5x + x2 = 0.00 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + -3.5x + x2 = 0.00 + -3.0625 -3.5x + x2 = 0.00 + -3.0625 Combine like terms: 0.00 + -3.0625 = -3.0625 -3.5x + x2 = -3.0625 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 = -3.0625 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -3.0625 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 3.0625 + -3.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -1.75) equal to 0.0000 and 0.0000.Subproblem 1
x + -1.75 = 0.0000 Simplifying x + -1.75 = 0.0000 Reorder the terms: -1.75 + x = 0.0000 Solving -1.75 + x = 0.0000 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 = 0.0000 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.0000 + 1.75 x = 0.0000 + 1.75 Combine like terms: 0.0000 + 1.75 = 1.75 x = 1.75 Simplifying x = 1.75Subproblem 2
x + -1.75 = 0.0000 Simplifying x + -1.75 = 0.0000 Reorder the terms: -1.75 + x = 0.0000 Solving -1.75 + x = 0.0000 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 = 0.0000 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.0000 + 1.75 x = 0.0000 + 1.75 Combine like terms: 0.0000 + 1.75 = 1.75 x = 1.75 Simplifying x = 1.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.75, 1.75}
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