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Simplifying 6x2 + -30x + 25 = 0 Reorder the terms: 25 + -30x + 6x2 = 0 Solving 25 + -30x + 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'. 4.166666667 + -5x + x2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + -5x + -4.166666667 + x2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + -5x + x2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + -4.166666667 -5x + x2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 -5x + x2 = -4.166666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.166666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.166666667 + 6.25 Combine like terms: -4.166666667 + 6.25 = 2.083333333 6.25 + -5x + x2 = 2.083333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x + -2.5) equal to 1.443375673 and -1.443375673.Subproblem 1
x + -2.5 = 1.443375673 Simplifying x + -2.5 = 1.443375673 Reorder the terms: -2.5 + x = 1.443375673 Solving -2.5 + x = 1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.443375673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.443375673 + 2.5 x = 1.443375673 + 2.5 Combine like terms: 1.443375673 + 2.5 = 3.943375673 x = 3.943375673 Simplifying x = 3.943375673Subproblem 2
x + -2.5 = -1.443375673 Simplifying x + -2.5 = -1.443375673 Reorder the terms: -2.5 + x = -1.443375673 Solving -2.5 + x = -1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.443375673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.443375673 + 2.5 x = -1.443375673 + 2.5 Combine like terms: -1.443375673 + 2.5 = 1.056624327 x = 1.056624327 Simplifying x = 1.056624327Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.943375673, 1.056624327}
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