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Simplifying 15x2 + -47x + -26 = 0 Reorder the terms: -26 + -47x + 15x2 = 0 Solving -26 + -47x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.733333333 + -3.133333333x + x2 = 0 Move the constant term to the right: Add '1.733333333' to each side of the equation. -1.733333333 + -3.133333333x + 1.733333333 + x2 = 0 + 1.733333333 Reorder the terms: -1.733333333 + 1.733333333 + -3.133333333x + x2 = 0 + 1.733333333 Combine like terms: -1.733333333 + 1.733333333 = 0.000000000 0.000000000 + -3.133333333x + x2 = 0 + 1.733333333 -3.133333333x + x2 = 0 + 1.733333333 Combine like terms: 0 + 1.733333333 = 1.733333333 -3.133333333x + x2 = 1.733333333 The x term is -3.133333333x. Take half its coefficient (-1.566666667). Square it (2.454444445) and add it to both sides. Add '2.454444445' to each side of the equation. -3.133333333x + 2.454444445 + x2 = 1.733333333 + 2.454444445 Reorder the terms: 2.454444445 + -3.133333333x + x2 = 1.733333333 + 2.454444445 Combine like terms: 1.733333333 + 2.454444445 = 4.187777778 2.454444445 + -3.133333333x + x2 = 4.187777778 Factor a perfect square on the left side: (x + -1.566666667)(x + -1.566666667) = 4.187777778 Calculate the square root of the right side: 2.046406064 Break this problem into two subproblems by setting (x + -1.566666667) equal to 2.046406064 and -2.046406064.Subproblem 1
x + -1.566666667 = 2.046406064 Simplifying x + -1.566666667 = 2.046406064 Reorder the terms: -1.566666667 + x = 2.046406064 Solving -1.566666667 + x = 2.046406064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.566666667' to each side of the equation. -1.566666667 + 1.566666667 + x = 2.046406064 + 1.566666667 Combine like terms: -1.566666667 + 1.566666667 = 0.000000000 0.000000000 + x = 2.046406064 + 1.566666667 x = 2.046406064 + 1.566666667 Combine like terms: 2.046406064 + 1.566666667 = 3.613072731 x = 3.613072731 Simplifying x = 3.613072731Subproblem 2
x + -1.566666667 = -2.046406064 Simplifying x + -1.566666667 = -2.046406064 Reorder the terms: -1.566666667 + x = -2.046406064 Solving -1.566666667 + x = -2.046406064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.566666667' to each side of the equation. -1.566666667 + 1.566666667 + x = -2.046406064 + 1.566666667 Combine like terms: -1.566666667 + 1.566666667 = 0.000000000 0.000000000 + x = -2.046406064 + 1.566666667 x = -2.046406064 + 1.566666667 Combine like terms: -2.046406064 + 1.566666667 = -0.479739397 x = -0.479739397 Simplifying x = -0.479739397Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.613072731, -0.479739397}
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