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Simplifying 36 + -56x + 15x2 = 0 Solving 36 + -56x + 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'. 2.4 + -3.733333333x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -3.733333333x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -3.733333333x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -3.733333333x + x2 = 0 + -2.4 -3.733333333x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -3.733333333x + x2 = -2.4 The x term is -3.733333333x. Take half its coefficient (-1.866666667). Square it (3.484444446) and add it to both sides. Add '3.484444446' to each side of the equation. -3.733333333x + 3.484444446 + x2 = -2.4 + 3.484444446 Reorder the terms: 3.484444446 + -3.733333333x + x2 = -2.4 + 3.484444446 Combine like terms: -2.4 + 3.484444446 = 1.084444446 3.484444446 + -3.733333333x + x2 = 1.084444446 Factor a perfect square on the left side: (x + -1.866666667)(x + -1.866666667) = 1.084444446 Calculate the square root of the right side: 1.041366624 Break this problem into two subproblems by setting (x + -1.866666667) equal to 1.041366624 and -1.041366624.Subproblem 1
x + -1.866666667 = 1.041366624 Simplifying x + -1.866666667 = 1.041366624 Reorder the terms: -1.866666667 + x = 1.041366624 Solving -1.866666667 + x = 1.041366624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + x = 1.041366624 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + x = 1.041366624 + 1.866666667 x = 1.041366624 + 1.866666667 Combine like terms: 1.041366624 + 1.866666667 = 2.908033291 x = 2.908033291 Simplifying x = 2.908033291Subproblem 2
x + -1.866666667 = -1.041366624 Simplifying x + -1.866666667 = -1.041366624 Reorder the terms: -1.866666667 + x = -1.041366624 Solving -1.866666667 + x = -1.041366624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + x = -1.041366624 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + x = -1.041366624 + 1.866666667 x = -1.041366624 + 1.866666667 Combine like terms: -1.041366624 + 1.866666667 = 0.825300043 x = 0.825300043 Simplifying x = 0.825300043Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.908033291, 0.825300043}
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