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Simplifying 15x2 + -3x + -2 = 0 Reorder the terms: -2 + -3x + 15x2 = 0 Solving -2 + -3x + 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 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + -0.2x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + -0.2x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + -0.2x + x2 = 0 + 0.1333333333 -0.2x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 -0.2x + x2 = 0.1333333333 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.1333333333 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.1333333333 + 0.01 Combine like terms: 0.1333333333 + 0.01 = 0.1433333333 0.01 + -0.2x + x2 = 0.1433333333 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.1433333333 Calculate the square root of the right side: 0.37859389 Break this problem into two subproblems by setting (x + -0.1) equal to 0.37859389 and -0.37859389.Subproblem 1
x + -0.1 = 0.37859389 Simplifying x + -0.1 = 0.37859389 Reorder the terms: -0.1 + x = 0.37859389 Solving -0.1 + x = 0.37859389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.37859389 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.37859389 + 0.1 x = 0.37859389 + 0.1 Combine like terms: 0.37859389 + 0.1 = 0.47859389 x = 0.47859389 Simplifying x = 0.47859389Subproblem 2
x + -0.1 = -0.37859389 Simplifying x + -0.1 = -0.37859389 Reorder the terms: -0.1 + x = -0.37859389 Solving -0.1 + x = -0.37859389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.37859389 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.37859389 + 0.1 x = -0.37859389 + 0.1 Combine like terms: -0.37859389 + 0.1 = -0.27859389 x = -0.27859389 Simplifying x = -0.27859389Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.47859389, -0.27859389}
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