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Simplifying x + 2x(x + 10) = 146 Reorder the terms: x + 2x(10 + x) = 146 x + (10 * 2x + x * 2x) = 146 x + (20x + 2x2) = 146 Combine like terms: x + 20x = 21x 21x + 2x2 = 146 Solving 21x + 2x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + 21x + 2x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -73 + 10.5x + x2 = 0 Move the constant term to the right: Add '73' to each side of the equation. -73 + 10.5x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 10.5x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 10.5x + x2 = 0 + 73 10.5x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 10.5x + x2 = 73 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 73 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 73 + 27.5625 Combine like terms: 73 + 27.5625 = 100.5625 27.5625 + 10.5x + x2 = 100.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 100.5625 Calculate the square root of the right side: 10.02808556 Break this problem into two subproblems by setting (x + 5.25) equal to 10.02808556 and -10.02808556.Subproblem 1
x + 5.25 = 10.02808556 Simplifying x + 5.25 = 10.02808556 Reorder the terms: 5.25 + x = 10.02808556 Solving 5.25 + x = 10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 10.02808556 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 10.02808556 + -5.25 x = 10.02808556 + -5.25 Combine like terms: 10.02808556 + -5.25 = 4.77808556 x = 4.77808556 Simplifying x = 4.77808556Subproblem 2
x + 5.25 = -10.02808556 Simplifying x + 5.25 = -10.02808556 Reorder the terms: 5.25 + x = -10.02808556 Solving 5.25 + x = -10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -10.02808556 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -10.02808556 + -5.25 x = -10.02808556 + -5.25 Combine like terms: -10.02808556 + -5.25 = -15.27808556 x = -15.27808556 Simplifying x = -15.27808556Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.77808556, -15.27808556}
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