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Simplifying 4x2 + 18x + 81 = 120 Reorder the terms: 81 + 18x + 4x2 = 120 Solving 81 + 18x + 4x2 = 120 Solving for variable 'x'. Reorder the terms: 81 + -120 + 18x + 4x2 = 120 + -120 Combine like terms: 81 + -120 = -39 -39 + 18x + 4x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -39 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + 4.5x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + 4.5x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + 4.5x + x2 = 0 + 9.75 4.5x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 4.5x + x2 = 9.75 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 = 9.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 9.75 + 5.0625 Combine like terms: 9.75 + 5.0625 = 14.8125 5.0625 + 4.5x + x2 = 14.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 14.8125 Calculate the square root of the right side: 3.84870108 Break this problem into two subproblems by setting (x + 2.25) equal to 3.84870108 and -3.84870108.Subproblem 1
x + 2.25 = 3.84870108 Simplifying x + 2.25 = 3.84870108 Reorder the terms: 2.25 + x = 3.84870108 Solving 2.25 + x = 3.84870108 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 = 3.84870108 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.84870108 + -2.25 x = 3.84870108 + -2.25 Combine like terms: 3.84870108 + -2.25 = 1.59870108 x = 1.59870108 Simplifying x = 1.59870108Subproblem 2
x + 2.25 = -3.84870108 Simplifying x + 2.25 = -3.84870108 Reorder the terms: 2.25 + x = -3.84870108 Solving 2.25 + x = -3.84870108 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 = -3.84870108 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.84870108 + -2.25 x = -3.84870108 + -2.25 Combine like terms: -3.84870108 + -2.25 = -6.09870108 x = -6.09870108 Simplifying x = -6.09870108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.59870108, -6.09870108}
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