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Simplifying 5x2 + 15x + 3 = 0 Reorder the terms: 3 + 15x + 5x2 = 0 Solving 3 + 15x + 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 + 3x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 3x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 3x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 3x + x2 = 0 + -0.6 3x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 3x + x2 = -0.6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.6 + 2.25 Combine like terms: -0.6 + 2.25 = 1.65 2.25 + 3x + x2 = 1.65 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting (x + 1.5) equal to 1.284523258 and -1.284523258.Subproblem 1
x + 1.5 = 1.284523258 Simplifying x + 1.5 = 1.284523258 Reorder the terms: 1.5 + x = 1.284523258 Solving 1.5 + x = 1.284523258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.284523258 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.284523258 + -1.5 x = 1.284523258 + -1.5 Combine like terms: 1.284523258 + -1.5 = -0.215476742 x = -0.215476742 Simplifying x = -0.215476742Subproblem 2
x + 1.5 = -1.284523258 Simplifying x + 1.5 = -1.284523258 Reorder the terms: 1.5 + x = -1.284523258 Solving 1.5 + x = -1.284523258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.284523258 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.284523258 + -1.5 x = -1.284523258 + -1.5 Combine like terms: -1.284523258 + -1.5 = -2.784523258 x = -2.784523258 Simplifying x = -2.784523258Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.215476742, -2.784523258}
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