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Simplifying 15x2 + -18x + 1 = 0 Reorder the terms: 1 + -18x + 15x2 = 0 Solving 1 + -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'. 0.06666666667 + -1.2x + x2 = 0 Move the constant term to the right: Add '-0.06666666667' to each side of the equation. 0.06666666667 + -1.2x + -0.06666666667 + x2 = 0 + -0.06666666667 Reorder the terms: 0.06666666667 + -0.06666666667 + -1.2x + x2 = 0 + -0.06666666667 Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000 0.00000000000 + -1.2x + x2 = 0 + -0.06666666667 -1.2x + x2 = 0 + -0.06666666667 Combine like terms: 0 + -0.06666666667 = -0.06666666667 -1.2x + x2 = -0.06666666667 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 = -0.06666666667 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.06666666667 + 0.36 Combine like terms: -0.06666666667 + 0.36 = 0.29333333333 0.36 + -1.2x + x2 = 0.29333333333 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.29333333333 Calculate the square root of the right side: 0.54160256 Break this problem into two subproblems by setting (x + -0.6) equal to 0.54160256 and -0.54160256.Subproblem 1
x + -0.6 = 0.54160256 Simplifying x + -0.6 = 0.54160256 Reorder the terms: -0.6 + x = 0.54160256 Solving -0.6 + x = 0.54160256 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 = 0.54160256 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.54160256 + 0.6 x = 0.54160256 + 0.6 Combine like terms: 0.54160256 + 0.6 = 1.14160256 x = 1.14160256 Simplifying x = 1.14160256Subproblem 2
x + -0.6 = -0.54160256 Simplifying x + -0.6 = -0.54160256 Reorder the terms: -0.6 + x = -0.54160256 Solving -0.6 + x = -0.54160256 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 = -0.54160256 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.54160256 + 0.6 x = -0.54160256 + 0.6 Combine like terms: -0.54160256 + 0.6 = 0.05839744 x = 0.05839744 Simplifying x = 0.05839744Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.14160256, 0.05839744}
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