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Simplifying 5x2 + 18x + 3 = 0 Reorder the terms: 3 + 18x + 5x2 = 0 Solving 3 + 18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 3.6x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 3.6x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 3.6x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 3.6x + x2 = 0 + -0.6 3.6x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 3.6x + x2 = -0.6 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -0.6 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -0.6 + 3.24 Combine like terms: -0.6 + 3.24 = 2.64 3.24 + 3.6x + x2 = 2.64 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (x + 1.8) equal to 1.624807681 and -1.624807681.Subproblem 1
x + 1.8 = 1.624807681 Simplifying x + 1.8 = 1.624807681 Reorder the terms: 1.8 + x = 1.624807681 Solving 1.8 + x = 1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.624807681 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.624807681 + -1.8 x = 1.624807681 + -1.8 Combine like terms: 1.624807681 + -1.8 = -0.175192319 x = -0.175192319 Simplifying x = -0.175192319Subproblem 2
x + 1.8 = -1.624807681 Simplifying x + 1.8 = -1.624807681 Reorder the terms: 1.8 + x = -1.624807681 Solving 1.8 + x = -1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.624807681 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.624807681 + -1.8 x = -1.624807681 + -1.8 Combine like terms: -1.624807681 + -1.8 = -3.424807681 x = -3.424807681 Simplifying x = -3.424807681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.175192319, -3.424807681}
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