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Simplifying 25 = 9x2 + -30x Reorder the terms: 25 = -30x + 9x2 Solving 25 = -30x + 9x2 Solving for variable 'x'. Reorder the terms: 25 + 30x + -9x2 = -30x + 30x + 9x2 + -9x2 Combine like terms: -30x + 30x = 0 25 + 30x + -9x2 = 0 + 9x2 + -9x2 25 + 30x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 25 + 30x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.777777778 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -3.333333333x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -3.333333333x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + 2.777777778 -3.333333333x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -3.333333333x + x2 = 2.777777778 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 2.777777778 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 2.777777778 + 2.777777779 Combine like terms: 2.777777778 + 2.777777779 = 5.555555557 2.777777779 + -3.333333333x + x2 = 5.555555557 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 5.555555557 Calculate the square root of the right side: 2.357022604 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.357022604 and -2.357022604.Subproblem 1
x + -1.666666667 = 2.357022604 Simplifying x + -1.666666667 = 2.357022604 Reorder the terms: -1.666666667 + x = 2.357022604 Solving -1.666666667 + x = 2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 2.357022604 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.357022604 + 1.666666667 x = 2.357022604 + 1.666666667 Combine like terms: 2.357022604 + 1.666666667 = 4.023689271 x = 4.023689271 Simplifying x = 4.023689271Subproblem 2
x + -1.666666667 = -2.357022604 Simplifying x + -1.666666667 = -2.357022604 Reorder the terms: -1.666666667 + x = -2.357022604 Solving -1.666666667 + x = -2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -2.357022604 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.357022604 + 1.666666667 x = -2.357022604 + 1.666666667 Combine like terms: -2.357022604 + 1.666666667 = -0.690355937 x = -0.690355937 Simplifying x = -0.690355937Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.023689271, -0.690355937}
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