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Simplifying 15x2 + -47x + 30 = 0 Reorder the terms: 30 + -47x + 15x2 = 0 Solving 30 + -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'. 2 + -3.133333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.133333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.133333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.133333333x + x2 = 0 + -2 -3.133333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.133333333x + x2 = -2 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 = -2 + 2.454444445 Reorder the terms: 2.454444445 + -3.133333333x + x2 = -2 + 2.454444445 Combine like terms: -2 + 2.454444445 = 0.454444445 2.454444445 + -3.133333333x + x2 = 0.454444445 Factor a perfect square on the left side: (x + -1.566666667)(x + -1.566666667) = 0.454444445 Calculate the square root of the right side: 0.674124948 Break this problem into two subproblems by setting (x + -1.566666667) equal to 0.674124948 and -0.674124948.Subproblem 1
x + -1.566666667 = 0.674124948 Simplifying x + -1.566666667 = 0.674124948 Reorder the terms: -1.566666667 + x = 0.674124948 Solving -1.566666667 + x = 0.674124948 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 = 0.674124948 + 1.566666667 Combine like terms: -1.566666667 + 1.566666667 = 0.000000000 0.000000000 + x = 0.674124948 + 1.566666667 x = 0.674124948 + 1.566666667 Combine like terms: 0.674124948 + 1.566666667 = 2.240791615 x = 2.240791615 Simplifying x = 2.240791615Subproblem 2
x + -1.566666667 = -0.674124948 Simplifying x + -1.566666667 = -0.674124948 Reorder the terms: -1.566666667 + x = -0.674124948 Solving -1.566666667 + x = -0.674124948 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 = -0.674124948 + 1.566666667 Combine like terms: -1.566666667 + 1.566666667 = 0.000000000 0.000000000 + x = -0.674124948 + 1.566666667 x = -0.674124948 + 1.566666667 Combine like terms: -0.674124948 + 1.566666667 = 0.892541719 x = 0.892541719 Simplifying x = 0.892541719Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.240791615, 0.892541719}
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