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Simplifying 0 = 6x2 + 10x + -25 Reorder the terms: 0 = -25 + 10x + 6x2 Solving 0 = -25 + 10x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -10x + -6x2 = -25 + 10x + 6x2 + 25 + -10x + -6x2 Reorder the terms: 25 + -10x + -6x2 = -25 + 25 + 10x + -10x + 6x2 + -6x2 Combine like terms: -25 + 25 = 0 25 + -10x + -6x2 = 0 + 10x + -10x + 6x2 + -6x2 25 + -10x + -6x2 = 10x + -10x + 6x2 + -6x2 Combine like terms: 10x + -10x = 0 25 + -10x + -6x2 = 0 + 6x2 + -6x2 25 + -10x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 25 + -10x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -4.166666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 1.666666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 1.666666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 4.166666667 1.666666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 1.666666667x + x2 = 4.166666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 4.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 4.166666667 + 0.6944444447 Combine like terms: 4.166666667 + 0.6944444447 = 4.8611111117 0.6944444447 + 1.666666667x + x2 = 4.8611111117 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 4.8611111117 Calculate the square root of the right side: 2.204792759 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.204792759 and -2.204792759.Subproblem 1
x + 0.8333333335 = 2.204792759 Simplifying x + 0.8333333335 = 2.204792759 Reorder the terms: 0.8333333335 + x = 2.204792759 Solving 0.8333333335 + x = 2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.204792759 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.204792759 + -0.8333333335 x = 2.204792759 + -0.8333333335 Combine like terms: 2.204792759 + -0.8333333335 = 1.3714594255 x = 1.3714594255 Simplifying x = 1.3714594255Subproblem 2
x + 0.8333333335 = -2.204792759 Simplifying x + 0.8333333335 = -2.204792759 Reorder the terms: 0.8333333335 + x = -2.204792759 Solving 0.8333333335 + x = -2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.204792759 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.204792759 + -0.8333333335 x = -2.204792759 + -0.8333333335 Combine like terms: -2.204792759 + -0.8333333335 = -3.0381260925 x = -3.0381260925 Simplifying x = -3.0381260925Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3714594255, -3.0381260925}
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