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Simplifying 4x2 + 36x + 71 = 0 Reorder the terms: 71 + 36x + 4x2 = 0 Solving 71 + 36x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 17.75 + 9x + x2 = 0 Move the constant term to the right: Add '-17.75' to each side of the equation. 17.75 + 9x + -17.75 + x2 = 0 + -17.75 Reorder the terms: 17.75 + -17.75 + 9x + x2 = 0 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + 9x + x2 = 0 + -17.75 9x + x2 = 0 + -17.75 Combine like terms: 0 + -17.75 = -17.75 9x + x2 = -17.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -17.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -17.75 + 20.25 Combine like terms: -17.75 + 20.25 = 2.5 20.25 + 9x + x2 = 2.5 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + 4.5) equal to 1.58113883 and -1.58113883.Subproblem 1
x + 4.5 = 1.58113883 Simplifying x + 4.5 = 1.58113883 Reorder the terms: 4.5 + x = 1.58113883 Solving 4.5 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 1.58113883 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 1.58113883 + -4.5 x = 1.58113883 + -4.5 Combine like terms: 1.58113883 + -4.5 = -2.91886117 x = -2.91886117 Simplifying x = -2.91886117Subproblem 2
x + 4.5 = -1.58113883 Simplifying x + 4.5 = -1.58113883 Reorder the terms: 4.5 + x = -1.58113883 Solving 4.5 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -1.58113883 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -1.58113883 + -4.5 x = -1.58113883 + -4.5 Combine like terms: -1.58113883 + -4.5 = -6.08113883 x = -6.08113883 Simplifying x = -6.08113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.91886117, -6.08113883}
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