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Simplifying 3x2 + x = 375 Reorder the terms: x + 3x2 = 375 Solving x + 3x2 = 375 Solving for variable 'x'. Reorder the terms: -375 + x + 3x2 = 375 + -375 Combine like terms: 375 + -375 = 0 -375 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -125 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 0.3333333333x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 0.3333333333x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 0.3333333333x + x2 = 0 + 125 0.3333333333x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 0.3333333333x + x2 = 125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 125 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 125 + 0.25 Combine like terms: 125 + 0.25 = 125.25 0.25 + 0.3333333333x + x2 = 125.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 125.25 Calculate the square root of the right side: 11.191514643 Break this problem into two subproblems by setting (x + 0.5) equal to 11.191514643 and -11.191514643.Subproblem 1
x + 0.5 = 11.191514643 Simplifying x + 0.5 = 11.191514643 Reorder the terms: 0.5 + x = 11.191514643 Solving 0.5 + x = 11.191514643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.191514643 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.191514643 + -0.5 x = 11.191514643 + -0.5 Combine like terms: 11.191514643 + -0.5 = 10.691514643 x = 10.691514643 Simplifying x = 10.691514643Subproblem 2
x + 0.5 = -11.191514643 Simplifying x + 0.5 = -11.191514643 Reorder the terms: 0.5 + x = -11.191514643 Solving 0.5 + x = -11.191514643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.191514643 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.191514643 + -0.5 x = -11.191514643 + -0.5 Combine like terms: -11.191514643 + -0.5 = -11.691514643 x = -11.691514643 Simplifying x = -11.691514643Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.691514643, -11.691514643}
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