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Simplifying 0.25x2 + 0.5x + 0.25 + -4x + 11 = 0 Reorder the terms: 0.25 + 11 + 0.5x + -4x + 0.25x2 = 0 Combine like terms: 0.25 + 11 = 11.25 11.25 + 0.5x + -4x + 0.25x2 = 0 Combine like terms: 0.5x + -4x = -3.5x 11.25 + -3.5x + 0.25x2 = 0 Solving 11.25 + -3.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 45 + -14x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -14x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -14x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -14x + x2 = 0 + -45 -14x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -14x + x2 = -45 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -45 + 49 Reorder the terms: 49 + -14x + x2 = -45 + 49 Combine like terms: -45 + 49 = 4 49 + -14x + x2 = 4 Factor a perfect square on the left side: (x + -7)(x + -7) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -7) equal to 2 and -2.Subproblem 1
x + -7 = 2 Simplifying x + -7 = 2 Reorder the terms: -7 + x = 2 Solving -7 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 2 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2 + 7 x = 2 + 7 Combine like terms: 2 + 7 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -7 = -2 Simplifying x + -7 = -2 Reorder the terms: -7 + x = -2 Solving -7 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -2 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2 + 7 x = -2 + 7 Combine like terms: -2 + 7 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, 5}
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