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Simplifying 3x(90 + -1x) = 50 (90 * 3x + -1x * 3x) = 50 (270x + -3x2) = 50 Solving 270x + -3x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 270x + -3x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 270x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 16.66666667 + -90x + x2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -90x + -16.66666667 + x2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -90x + x2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -90x + x2 = 0 + -16.66666667 -90x + x2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -90x + x2 = -16.66666667 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -16.66666667 + 2025 Reorder the terms: 2025 + -90x + x2 = -16.66666667 + 2025 Combine like terms: -16.66666667 + 2025 = 2008.33333333 2025 + -90x + x2 = 2008.33333333 Factor a perfect square on the left side: (x + -45)(x + -45) = 2008.33333333 Calculate the square root of the right side: 44.814432199 Break this problem into two subproblems by setting (x + -45) equal to 44.814432199 and -44.814432199.Subproblem 1
x + -45 = 44.814432199 Simplifying x + -45 = 44.814432199 Reorder the terms: -45 + x = 44.814432199 Solving -45 + x = 44.814432199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 44.814432199 + 45 Combine like terms: -45 + 45 = 0 0 + x = 44.814432199 + 45 x = 44.814432199 + 45 Combine like terms: 44.814432199 + 45 = 89.814432199 x = 89.814432199 Simplifying x = 89.814432199Subproblem 2
x + -45 = -44.814432199 Simplifying x + -45 = -44.814432199 Reorder the terms: -45 + x = -44.814432199 Solving -45 + x = -44.814432199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -44.814432199 + 45 Combine like terms: -45 + 45 = 0 0 + x = -44.814432199 + 45 x = -44.814432199 + 45 Combine like terms: -44.814432199 + 45 = 0.185567801 x = 0.185567801 Simplifying x = 0.185567801Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.814432199, 0.185567801}
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