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Simplifying 29x + x2 = 750 Solving 29x + x2 = 750 Solving for variable 'x'. Reorder the terms: -750 + 29x + x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -750 + 29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + 29x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + 29x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + 29x + x2 = 0 + 750 29x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 29x + x2 = 750 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 750 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 750 + 210.25 Combine like terms: 750 + 210.25 = 960.25 210.25 + 29x + x2 = 960.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 960.25 Calculate the square root of the right side: 30.987900865 Break this problem into two subproblems by setting (x + 14.5) equal to 30.987900865 and -30.987900865.Subproblem 1
x + 14.5 = 30.987900865 Simplifying x + 14.5 = 30.987900865 Reorder the terms: 14.5 + x = 30.987900865 Solving 14.5 + x = 30.987900865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 30.987900865 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 30.987900865 + -14.5 x = 30.987900865 + -14.5 Combine like terms: 30.987900865 + -14.5 = 16.487900865 x = 16.487900865 Simplifying x = 16.487900865Subproblem 2
x + 14.5 = -30.987900865 Simplifying x + 14.5 = -30.987900865 Reorder the terms: 14.5 + x = -30.987900865 Solving 14.5 + x = -30.987900865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -30.987900865 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -30.987900865 + -14.5 x = -30.987900865 + -14.5 Combine like terms: -30.987900865 + -14.5 = -45.487900865 x = -45.487900865 Simplifying x = -45.487900865Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.487900865, -45.487900865}
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