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Simplifying 4x2 + 47x = -91 Reorder the terms: 47x + 4x2 = -91 Solving 47x + 4x2 = -91 Solving for variable 'x'. Reorder the terms: 91 + 47x + 4x2 = -91 + 91 Combine like terms: -91 + 91 = 0 91 + 47x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 22.75 + 11.75x + x2 = 0 Move the constant term to the right: Add '-22.75' to each side of the equation. 22.75 + 11.75x + -22.75 + x2 = 0 + -22.75 Reorder the terms: 22.75 + -22.75 + 11.75x + x2 = 0 + -22.75 Combine like terms: 22.75 + -22.75 = 0.00 0.00 + 11.75x + x2 = 0 + -22.75 11.75x + x2 = 0 + -22.75 Combine like terms: 0 + -22.75 = -22.75 11.75x + x2 = -22.75 The x term is 11.75x. Take half its coefficient (5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. 11.75x + 34.515625 + x2 = -22.75 + 34.515625 Reorder the terms: 34.515625 + 11.75x + x2 = -22.75 + 34.515625 Combine like terms: -22.75 + 34.515625 = 11.765625 34.515625 + 11.75x + x2 = 11.765625 Factor a perfect square on the left side: (x + 5.875)(x + 5.875) = 11.765625 Calculate the square root of the right side: 3.430105684 Break this problem into two subproblems by setting (x + 5.875) equal to 3.430105684 and -3.430105684.Subproblem 1
x + 5.875 = 3.430105684 Simplifying x + 5.875 = 3.430105684 Reorder the terms: 5.875 + x = 3.430105684 Solving 5.875 + x = 3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = 3.430105684 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = 3.430105684 + -5.875 x = 3.430105684 + -5.875 Combine like terms: 3.430105684 + -5.875 = -2.444894316 x = -2.444894316 Simplifying x = -2.444894316Subproblem 2
x + 5.875 = -3.430105684 Simplifying x + 5.875 = -3.430105684 Reorder the terms: 5.875 + x = -3.430105684 Solving 5.875 + x = -3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = -3.430105684 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = -3.430105684 + -5.875 x = -3.430105684 + -5.875 Combine like terms: -3.430105684 + -5.875 = -9.305105684 x = -9.305105684 Simplifying x = -9.305105684Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.444894316, -9.305105684}
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