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Simplifying 15x2 + 18x + -2 = 0 Reorder the terms: -2 + 18x + 15x2 = 0 Solving -2 + 18x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.1333333333 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + 1.2x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + 1.2x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + 1.2x + x2 = 0 + 0.1333333333 1.2x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 1.2x + x2 = 0.1333333333 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 0.1333333333 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.1333333333 + 0.36 Combine like terms: 0.1333333333 + 0.36 = 0.4933333333 0.36 + 1.2x + x2 = 0.4933333333 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.4933333333 Calculate the square root of the right side: 0.702376917 Break this problem into two subproblems by setting (x + 0.6) equal to 0.702376917 and -0.702376917.Subproblem 1
x + 0.6 = 0.702376917 Simplifying x + 0.6 = 0.702376917 Reorder the terms: 0.6 + x = 0.702376917 Solving 0.6 + x = 0.702376917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.702376917 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.702376917 + -0.6 x = 0.702376917 + -0.6 Combine like terms: 0.702376917 + -0.6 = 0.102376917 x = 0.102376917 Simplifying x = 0.102376917Subproblem 2
x + 0.6 = -0.702376917 Simplifying x + 0.6 = -0.702376917 Reorder the terms: 0.6 + x = -0.702376917 Solving 0.6 + x = -0.702376917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.702376917 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.702376917 + -0.6 x = -0.702376917 + -0.6 Combine like terms: -0.702376917 + -0.6 = -1.302376917 x = -1.302376917 Simplifying x = -1.302376917Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.102376917, -1.302376917}
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