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Simplifying 0 = 2 + 15x + 5x2 Solving 0 = 2 + 15x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -15x + -5x2 = 2 + 15x + 5x2 + -2 + -15x + -5x2 Reorder the terms: -2 + -15x + -5x2 = 2 + -2 + 15x + -15x + 5x2 + -5x2 Combine like terms: 2 + -2 = 0 -2 + -15x + -5x2 = 0 + 15x + -15x + 5x2 + -5x2 -2 + -15x + -5x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 -2 + -15x + -5x2 = 0 + 5x2 + -5x2 -2 + -15x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -2 + -15x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 15x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 15x + 5x2 = 0 Solving 2 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 3x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 3x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 3x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 3x + x2 = 0 + -0.4 3x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 3x + x2 = -0.4 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 = -0.4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.4 + 2.25 Combine like terms: -0.4 + 2.25 = 1.85 2.25 + 3x + x2 = 1.85 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.85 Calculate the square root of the right side: 1.360147051 Break this problem into two subproblems by setting (x + 1.5) equal to 1.360147051 and -1.360147051.Subproblem 1
x + 1.5 = 1.360147051 Simplifying x + 1.5 = 1.360147051 Reorder the terms: 1.5 + x = 1.360147051 Solving 1.5 + x = 1.360147051 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 = 1.360147051 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.360147051 + -1.5 x = 1.360147051 + -1.5 Combine like terms: 1.360147051 + -1.5 = -0.139852949 x = -0.139852949 Simplifying x = -0.139852949Subproblem 2
x + 1.5 = -1.360147051 Simplifying x + 1.5 = -1.360147051 Reorder the terms: 1.5 + x = -1.360147051 Solving 1.5 + x = -1.360147051 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 = -1.360147051 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.360147051 + -1.5 x = -1.360147051 + -1.5 Combine like terms: -1.360147051 + -1.5 = -2.860147051 x = -2.860147051 Simplifying x = -2.860147051Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.139852949, -2.860147051}Solution
x = {-0.139852949, -2.860147051}
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