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Simplifying 25x = -20 + -6x2 Solving 25x = -20 + -6x2 Solving for variable 'x'. Reorder the terms: 20 + 25x + 6x2 = -20 + -6x2 + 20 + 6x2 Reorder the terms: 20 + 25x + 6x2 = -20 + 20 + -6x2 + 6x2 Combine like terms: -20 + 20 = 0 20 + 25x + 6x2 = 0 + -6x2 + 6x2 20 + 25x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 20 + 25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.333333333 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 4.166666667x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 4.166666667x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 4.166666667x + x2 = 0 + -3.333333333 4.166666667x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 4.166666667x + x2 = -3.333333333 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 = -3.333333333 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = -3.333333333 + 4.340277781 Combine like terms: -3.333333333 + 4.340277781 = 1.006944448 4.340277781 + 4.166666667x + x2 = 1.006944448 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 1.006944448 Calculate the square root of the right side: 1.003466217 Break this problem into two subproblems by setting (x + 2.083333334) equal to 1.003466217 and -1.003466217.Subproblem 1
x + 2.083333334 = 1.003466217 Simplifying x + 2.083333334 = 1.003466217 Reorder the terms: 2.083333334 + x = 1.003466217 Solving 2.083333334 + x = 1.003466217 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 = 1.003466217 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 1.003466217 + -2.083333334 x = 1.003466217 + -2.083333334 Combine like terms: 1.003466217 + -2.083333334 = -1.079867117 x = -1.079867117 Simplifying x = -1.079867117Subproblem 2
x + 2.083333334 = -1.003466217 Simplifying x + 2.083333334 = -1.003466217 Reorder the terms: 2.083333334 + x = -1.003466217 Solving 2.083333334 + x = -1.003466217 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 = -1.003466217 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -1.003466217 + -2.083333334 x = -1.003466217 + -2.083333334 Combine like terms: -1.003466217 + -2.083333334 = -3.086799551 x = -3.086799551 Simplifying x = -3.086799551Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.079867117, -3.086799551}
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