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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 = 2.85 2.25 + 3x + x2 = 2.85 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (x + 1.5) equal to 1.688194302 and -1.688194302.Subproblem 1
x + 1.5 = 1.688194302 Simplifying x + 1.5 = 1.688194302 Reorder the terms: 1.5 + x = 1.688194302 Solving 1.5 + x = 1.688194302 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 = 1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.688194302 + -1.5 x = 1.688194302 + -1.5 Combine like terms: 1.688194302 + -1.5 = 0.188194302 x = 0.188194302 Simplifying x = 0.188194302Subproblem 2
x + 1.5 = -1.688194302 Simplifying x + 1.5 = -1.688194302 Reorder the terms: 1.5 + x = -1.688194302 Solving 1.5 + x = -1.688194302 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 = -1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.688194302 + -1.5 x = -1.688194302 + -1.5 Combine like terms: -1.688194302 + -1.5 = -3.188194302 x = -3.188194302 Simplifying x = -3.188194302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.188194302, -3.188194302}
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