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Simplifying x2 + x + 0.5x = 100 Reorder the terms: x + 0.5x + x2 = 100 Combine like terms: x + 0.5x = 1.5x 1.5x + x2 = 100 Solving 1.5x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 1.5x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 1.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 1.5x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 1.5x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 1.5x + x2 = 0 + 100 1.5x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 1.5x + x2 = 100 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 100 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 100 + 0.5625 Combine like terms: 100 + 0.5625 = 100.5625 0.5625 + 1.5x + x2 = 100.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 100.5625 Calculate the square root of the right side: 10.02808556 Break this problem into two subproblems by setting (x + 0.75) equal to 10.02808556 and -10.02808556.Subproblem 1
x + 0.75 = 10.02808556 Simplifying x + 0.75 = 10.02808556 Reorder the terms: 0.75 + x = 10.02808556 Solving 0.75 + x = 10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.02808556 + -0.75 x = 10.02808556 + -0.75 Combine like terms: 10.02808556 + -0.75 = 9.27808556 x = 9.27808556 Simplifying x = 9.27808556Subproblem 2
x + 0.75 = -10.02808556 Simplifying x + 0.75 = -10.02808556 Reorder the terms: 0.75 + x = -10.02808556 Solving 0.75 + x = -10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.02808556 + -0.75 x = -10.02808556 + -0.75 Combine like terms: -10.02808556 + -0.75 = -10.77808556 x = -10.77808556 Simplifying x = -10.77808556Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.27808556, -10.77808556}
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