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Simplifying 4x2 + 18x + -31 = 0 Reorder the terms: -31 + 18x + 4x2 = 0 Solving -31 + 18x + 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'. -7.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + 4.5x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + 4.5x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + 4.5x + x2 = 0 + 7.75 4.5x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 4.5x + x2 = 7.75 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 7.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 7.75 + 5.0625 Combine like terms: 7.75 + 5.0625 = 12.8125 5.0625 + 4.5x + x2 = 12.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 12.8125 Calculate the square root of the right side: 3.579455266 Break this problem into two subproblems by setting (x + 2.25) equal to 3.579455266 and -3.579455266.Subproblem 1
x + 2.25 = 3.579455266 Simplifying x + 2.25 = 3.579455266 Reorder the terms: 2.25 + x = 3.579455266 Solving 2.25 + x = 3.579455266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.579455266 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.579455266 + -2.25 x = 3.579455266 + -2.25 Combine like terms: 3.579455266 + -2.25 = 1.329455266 x = 1.329455266 Simplifying x = 1.329455266Subproblem 2
x + 2.25 = -3.579455266 Simplifying x + 2.25 = -3.579455266 Reorder the terms: 2.25 + x = -3.579455266 Solving 2.25 + x = -3.579455266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.579455266 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.579455266 + -2.25 x = -3.579455266 + -2.25 Combine like terms: -3.579455266 + -2.25 = -5.829455266 x = -5.829455266 Simplifying x = -5.829455266Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.329455266, -5.829455266}
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