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Simplifying 6x2 + -25x + 10 = 0 Reorder the terms: 10 + -25x + 6x2 = 0 Solving 10 + -25x + 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'. 1.666666667 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -4.166666667x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -4.166666667x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -4.166666667x + x2 = 0 + -1.666666667 -4.166666667x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -4.166666667x + x2 = -1.666666667 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = -1.666666667 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = -1.666666667 + 4.340277781 Combine like terms: -1.666666667 + 4.340277781 = 2.673611114 4.340277781 + -4.166666667x + x2 = 2.673611114 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 2.673611114 Calculate the square root of the right side: 1.635118073 Break this problem into two subproblems by setting (x + -2.083333334) equal to 1.635118073 and -1.635118073.Subproblem 1
x + -2.083333334 = 1.635118073 Simplifying x + -2.083333334 = 1.635118073 Reorder the terms: -2.083333334 + x = 1.635118073 Solving -2.083333334 + x = 1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 1.635118073 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 1.635118073 + 2.083333334 x = 1.635118073 + 2.083333334 Combine like terms: 1.635118073 + 2.083333334 = 3.718451407 x = 3.718451407 Simplifying x = 3.718451407Subproblem 2
x + -2.083333334 = -1.635118073 Simplifying x + -2.083333334 = -1.635118073 Reorder the terms: -2.083333334 + x = -1.635118073 Solving -2.083333334 + x = -1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -1.635118073 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -1.635118073 + 2.083333334 x = -1.635118073 + 2.083333334 Combine like terms: -1.635118073 + 2.083333334 = 0.448215261 x = 0.448215261 Simplifying x = 0.448215261Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.718451407, 0.448215261}
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