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Simplifying 0.75x2 + -15x + 25 = 0 Reorder the terms: 25 + -15x + 0.75x2 = 0 Solving 25 + -15x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. 33.33333333 + -20x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + -20x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + -20x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + -20x + x2 = 0 + -33.33333333 -20x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 -20x + x2 = -33.33333333 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -33.33333333 + 100 Reorder the terms: 100 + -20x + x2 = -33.33333333 + 100 Combine like terms: -33.33333333 + 100 = 66.66666667 100 + -20x + x2 = 66.66666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 66.66666667 Calculate the square root of the right side: 8.164965809 Break this problem into two subproblems by setting (x + -10) equal to 8.164965809 and -8.164965809.Subproblem 1
x + -10 = 8.164965809 Simplifying x + -10 = 8.164965809 Reorder the terms: -10 + x = 8.164965809 Solving -10 + x = 8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.164965809 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.164965809 + 10 x = 8.164965809 + 10 Combine like terms: 8.164965809 + 10 = 18.164965809 x = 18.164965809 Simplifying x = 18.164965809Subproblem 2
x + -10 = -8.164965809 Simplifying x + -10 = -8.164965809 Reorder the terms: -10 + x = -8.164965809 Solving -10 + x = -8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.164965809 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.164965809 + 10 x = -8.164965809 + 10 Combine like terms: -8.164965809 + 10 = 1.835034191 x = 1.835034191 Simplifying x = 1.835034191Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.164965809, 1.835034191}
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