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Simplifying 5x2 + -37x + 48 = 0 Reorder the terms: 48 + -37x + 5x2 = 0 Solving 48 + -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'. 9.6 + -7.4x + x2 = 0 Move the constant term to the right: Add '-9.6' to each side of the equation. 9.6 + -7.4x + -9.6 + x2 = 0 + -9.6 Reorder the terms: 9.6 + -9.6 + -7.4x + x2 = 0 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -7.4x + x2 = 0 + -9.6 -7.4x + x2 = 0 + -9.6 Combine like terms: 0 + -9.6 = -9.6 -7.4x + x2 = -9.6 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 = -9.6 + 13.69 Reorder the terms: 13.69 + -7.4x + x2 = -9.6 + 13.69 Combine like terms: -9.6 + 13.69 = 4.09 13.69 + -7.4x + x2 = 4.09 Factor a perfect square on the left side: (x + -3.7)(x + -3.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -3.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -3.7 = 2.022374842 Simplifying x + -3.7 = 2.022374842 Reorder the terms: -3.7 + x = 2.022374842 Solving -3.7 + x = 2.022374842 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 = 2.022374842 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = 2.022374842 + 3.7 x = 2.022374842 + 3.7 Combine like terms: 2.022374842 + 3.7 = 5.722374842 x = 5.722374842 Simplifying x = 5.722374842Subproblem 2
x + -3.7 = -2.022374842 Simplifying x + -3.7 = -2.022374842 Reorder the terms: -3.7 + x = -2.022374842 Solving -3.7 + x = -2.022374842 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 = -2.022374842 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = -2.022374842 + 3.7 x = -2.022374842 + 3.7 Combine like terms: -2.022374842 + 3.7 = 1.677625158 x = 1.677625158 Simplifying x = 1.677625158Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.722374842, 1.677625158}
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