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Simplifying 6x2 + 25x = 75 Reorder the terms: 25x + 6x2 = 75 Solving 25x + 6x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 25x + 6x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.5 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 4.166666667x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 4.166666667x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 4.166666667x + x2 = 0 + 12.5 4.166666667x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 4.166666667x + x2 = 12.5 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 = 12.5 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = 12.5 + 4.340277781 Combine like terms: 12.5 + 4.340277781 = 16.840277781 4.340277781 + 4.166666667x + x2 = 16.840277781 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 16.840277781 Calculate the square root of the right side: 4.103690751 Break this problem into two subproblems by setting (x + 2.083333334) equal to 4.103690751 and -4.103690751.Subproblem 1
x + 2.083333334 = 4.103690751 Simplifying x + 2.083333334 = 4.103690751 Reorder the terms: 2.083333334 + x = 4.103690751 Solving 2.083333334 + x = 4.103690751 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 = 4.103690751 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 4.103690751 + -2.083333334 x = 4.103690751 + -2.083333334 Combine like terms: 4.103690751 + -2.083333334 = 2.020357417 x = 2.020357417 Simplifying x = 2.020357417Subproblem 2
x + 2.083333334 = -4.103690751 Simplifying x + 2.083333334 = -4.103690751 Reorder the terms: 2.083333334 + x = -4.103690751 Solving 2.083333334 + x = -4.103690751 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 = -4.103690751 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -4.103690751 + -2.083333334 x = -4.103690751 + -2.083333334 Combine like terms: -4.103690751 + -2.083333334 = -6.187024085 x = -6.187024085 Simplifying x = -6.187024085Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.020357417, -6.187024085}
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