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Simplifying 6x2 + -15x + 2 = 0 Reorder the terms: 2 + -15x + 6x2 = 0 Solving 2 + -15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -2.5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -2.5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -2.5x + x2 = 0 + -0.3333333333 -2.5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -2.5x + x2 = -0.3333333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.3333333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.3333333333 + 1.5625 Combine like terms: -0.3333333333 + 1.5625 = 1.2291666667 1.5625 + -2.5x + x2 = 1.2291666667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.2291666667 Calculate the square root of the right side: 1.108677891 Break this problem into two subproblems by setting (x + -1.25) equal to 1.108677891 and -1.108677891.Subproblem 1
x + -1.25 = 1.108677891 Simplifying x + -1.25 = 1.108677891 Reorder the terms: -1.25 + x = 1.108677891 Solving -1.25 + x = 1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.108677891 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.108677891 + 1.25 x = 1.108677891 + 1.25 Combine like terms: 1.108677891 + 1.25 = 2.358677891 x = 2.358677891 Simplifying x = 2.358677891Subproblem 2
x + -1.25 = -1.108677891 Simplifying x + -1.25 = -1.108677891 Reorder the terms: -1.25 + x = -1.108677891 Solving -1.25 + x = -1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.108677891 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.108677891 + 1.25 x = -1.108677891 + 1.25 Combine like terms: -1.108677891 + 1.25 = 0.141322109 x = 0.141322109 Simplifying x = 0.141322109Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.358677891, 0.141322109}
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