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Simplifying 5x2 + -37x + 12 = 0 Reorder the terms: 12 + -37x + 5x2 = 0 Solving 12 + -37x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -7.4x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -7.4x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -7.4x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -7.4x + x2 = 0 + -2.4 -7.4x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -7.4x + x2 = -2.4 The x term is -7.4x. Take half its coefficient (-3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. -7.4x + 13.69 + x2 = -2.4 + 13.69 Reorder the terms: 13.69 + -7.4x + x2 = -2.4 + 13.69 Combine like terms: -2.4 + 13.69 = 11.29 13.69 + -7.4x + x2 = 11.29 Factor a perfect square on the left side: (x + -3.7)(x + -3.7) = 11.29 Calculate the square root of the right side: 3.360059523 Break this problem into two subproblems by setting (x + -3.7) equal to 3.360059523 and -3.360059523.Subproblem 1
x + -3.7 = 3.360059523 Simplifying x + -3.7 = 3.360059523 Reorder the terms: -3.7 + x = 3.360059523 Solving -3.7 + x = 3.360059523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = 3.360059523 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = 3.360059523 + 3.7 x = 3.360059523 + 3.7 Combine like terms: 3.360059523 + 3.7 = 7.060059523 x = 7.060059523 Simplifying x = 7.060059523Subproblem 2
x + -3.7 = -3.360059523 Simplifying x + -3.7 = -3.360059523 Reorder the terms: -3.7 + x = -3.360059523 Solving -3.7 + x = -3.360059523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = -3.360059523 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = -3.360059523 + 3.7 x = -3.360059523 + 3.7 Combine like terms: -3.360059523 + 3.7 = 0.339940477 x = 0.339940477 Simplifying x = 0.339940477Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.060059523, 0.339940477}
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