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Simplifying 6x2 + -1.75x = x + -0.25 Reorder the terms: -1.75x + 6x2 = x + -0.25 Reorder the terms: -1.75x + 6x2 = -0.25 + x Solving -1.75x + 6x2 = -0.25 + x Solving for variable 'x'. Reorder the terms: 0.25 + -1.75x + -1x + 6x2 = -0.25 + x + 0.25 + -1x Combine like terms: -1.75x + -1x = -2.75x 0.25 + -2.75x + 6x2 = -0.25 + x + 0.25 + -1x Reorder the terms: 0.25 + -2.75x + 6x2 = -0.25 + 0.25 + x + -1x Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -2.75x + 6x2 = 0.00 + x + -1x 0.25 + -2.75x + 6x2 = x + -1x Combine like terms: x + -1x = 0 0.25 + -2.75x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.04166666667 + -0.4583333333x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.4583333333x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + -0.4583333333x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + -0.4583333333x + x2 = 0 + -0.04166666667 -0.4583333333x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 -0.4583333333x + x2 = -0.04166666667 The x term is -0.4583333333x. Take half its coefficient (-0.2291666667). Square it (0.05251736113) and add it to both sides. Add '0.05251736113' to each side of the equation. -0.4583333333x + 0.05251736113 + x2 = -0.04166666667 + 0.05251736113 Reorder the terms: 0.05251736113 + -0.4583333333x + x2 = -0.04166666667 + 0.05251736113 Combine like terms: -0.04166666667 + 0.05251736113 = 0.01085069446 0.05251736113 + -0.4583333333x + x2 = 0.01085069446 Factor a perfect square on the left side: (x + -0.2291666667)(x + -0.2291666667) = 0.01085069446 Calculate the square root of the right side: 0.104166667 Break this problem into two subproblems by setting (x + -0.2291666667) equal to 0.104166667 and -0.104166667.Subproblem 1
x + -0.2291666667 = 0.104166667 Simplifying x + -0.2291666667 = 0.104166667 Reorder the terms: -0.2291666667 + x = 0.104166667 Solving -0.2291666667 + x = 0.104166667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + x = 0.104166667 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = 0.104166667 + 0.2291666667 x = 0.104166667 + 0.2291666667 Combine like terms: 0.104166667 + 0.2291666667 = 0.3333333337 x = 0.3333333337 Simplifying x = 0.3333333337Subproblem 2
x + -0.2291666667 = -0.104166667 Simplifying x + -0.2291666667 = -0.104166667 Reorder the terms: -0.2291666667 + x = -0.104166667 Solving -0.2291666667 + x = -0.104166667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + x = -0.104166667 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = -0.104166667 + 0.2291666667 x = -0.104166667 + 0.2291666667 Combine like terms: -0.104166667 + 0.2291666667 = 0.1249999997 x = 0.1249999997 Simplifying x = 0.1249999997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3333333337, 0.1249999997}
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