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Simplifying 4x2 + 18x + 3 = 0 Reorder the terms: 3 + 18x + 4x2 = 0 Solving 3 + 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'. 0.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 4.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 4.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 4.5x + x2 = 0 + -0.75 4.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 4.5x + x2 = -0.75 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 = -0.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -0.75 + 5.0625 Combine like terms: -0.75 + 5.0625 = 4.3125 5.0625 + 4.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + 2.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + 2.25 = 2.076655966 Simplifying x + 2.25 = 2.076655966 Reorder the terms: 2.25 + x = 2.076655966 Solving 2.25 + x = 2.076655966 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 = 2.076655966 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.076655966 + -2.25 x = 2.076655966 + -2.25 Combine like terms: 2.076655966 + -2.25 = -0.173344034 x = -0.173344034 Simplifying x = -0.173344034Subproblem 2
x + 2.25 = -2.076655966 Simplifying x + 2.25 = -2.076655966 Reorder the terms: 2.25 + x = -2.076655966 Solving 2.25 + x = -2.076655966 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 = -2.076655966 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.076655966 + -2.25 x = -2.076655966 + -2.25 Combine like terms: -2.076655966 + -2.25 = -4.326655966 x = -4.326655966 Simplifying x = -4.326655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.173344034, -4.326655966}
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