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Simplifying 56x2 + 155x + 71 = -5 + 7 Reorder the terms: 71 + 155x + 56x2 = -5 + 7 Combine like terms: -5 + 7 = 2 71 + 155x + 56x2 = 2 Solving 71 + 155x + 56x2 = 2 Solving for variable 'x'. Reorder the terms: 71 + -2 + 155x + 56x2 = 2 + -2 Combine like terms: 71 + -2 = 69 69 + 155x + 56x2 = 2 + -2 Combine like terms: 2 + -2 = 0 69 + 155x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 1.232142857 + 2.767857143x + x2 = 0 Move the constant term to the right: Add '-1.232142857' to each side of the equation. 1.232142857 + 2.767857143x + -1.232142857 + x2 = 0 + -1.232142857 Reorder the terms: 1.232142857 + -1.232142857 + 2.767857143x + x2 = 0 + -1.232142857 Combine like terms: 1.232142857 + -1.232142857 = 0.000000000 0.000000000 + 2.767857143x + x2 = 0 + -1.232142857 2.767857143x + x2 = 0 + -1.232142857 Combine like terms: 0 + -1.232142857 = -1.232142857 2.767857143x + x2 = -1.232142857 The x term is 2.767857143x. Take half its coefficient (1.383928572). Square it (1.915258292) and add it to both sides. Add '1.915258292' to each side of the equation. 2.767857143x + 1.915258292 + x2 = -1.232142857 + 1.915258292 Reorder the terms: 1.915258292 + 2.767857143x + x2 = -1.232142857 + 1.915258292 Combine like terms: -1.232142857 + 1.915258292 = 0.683115435 1.915258292 + 2.767857143x + x2 = 0.683115435 Factor a perfect square on the left side: (x + 1.383928572)(x + 1.383928572) = 0.683115435 Calculate the square root of the right side: 0.826507976 Break this problem into two subproblems by setting (x + 1.383928572) equal to 0.826507976 and -0.826507976.Subproblem 1
x + 1.383928572 = 0.826507976 Simplifying x + 1.383928572 = 0.826507976 Reorder the terms: 1.383928572 + x = 0.826507976 Solving 1.383928572 + x = 0.826507976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.383928572' to each side of the equation. 1.383928572 + -1.383928572 + x = 0.826507976 + -1.383928572 Combine like terms: 1.383928572 + -1.383928572 = 0.000000000 0.000000000 + x = 0.826507976 + -1.383928572 x = 0.826507976 + -1.383928572 Combine like terms: 0.826507976 + -1.383928572 = -0.557420596 x = -0.557420596 Simplifying x = -0.557420596Subproblem 2
x + 1.383928572 = -0.826507976 Simplifying x + 1.383928572 = -0.826507976 Reorder the terms: 1.383928572 + x = -0.826507976 Solving 1.383928572 + x = -0.826507976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.383928572' to each side of the equation. 1.383928572 + -1.383928572 + x = -0.826507976 + -1.383928572 Combine like terms: 1.383928572 + -1.383928572 = 0.000000000 0.000000000 + x = -0.826507976 + -1.383928572 x = -0.826507976 + -1.383928572 Combine like terms: -0.826507976 + -1.383928572 = -2.210436548 x = -2.210436548 Simplifying x = -2.210436548Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.557420596, -2.210436548}
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