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Simplifying 15x2 + -28x + 3 = 0 Reorder the terms: 3 + -28x + 15x2 = 0 Solving 3 + -28x + 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'. 0.2 + -1.866666667x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.866666667x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.866666667x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.866666667x + x2 = 0 + -0.2 -1.866666667x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.866666667x + x2 = -0.2 The x term is -1.866666667x. Take half its coefficient (-0.9333333335). Square it (0.8711111114) and add it to both sides. Add '0.8711111114' to each side of the equation. -1.866666667x + 0.8711111114 + x2 = -0.2 + 0.8711111114 Reorder the terms: 0.8711111114 + -1.866666667x + x2 = -0.2 + 0.8711111114 Combine like terms: -0.2 + 0.8711111114 = 0.6711111114 0.8711111114 + -1.866666667x + x2 = 0.6711111114 Factor a perfect square on the left side: (x + -0.9333333335)(x + -0.9333333335) = 0.6711111114 Calculate the square root of the right side: 0.819213715 Break this problem into two subproblems by setting (x + -0.9333333335) equal to 0.819213715 and -0.819213715.Subproblem 1
x + -0.9333333335 = 0.819213715 Simplifying x + -0.9333333335 = 0.819213715 Reorder the terms: -0.9333333335 + x = 0.819213715 Solving -0.9333333335 + x = 0.819213715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = 0.819213715 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = 0.819213715 + 0.9333333335 x = 0.819213715 + 0.9333333335 Combine like terms: 0.819213715 + 0.9333333335 = 1.7525470485 x = 1.7525470485 Simplifying x = 1.7525470485Subproblem 2
x + -0.9333333335 = -0.819213715 Simplifying x + -0.9333333335 = -0.819213715 Reorder the terms: -0.9333333335 + x = -0.819213715 Solving -0.9333333335 + x = -0.819213715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = -0.819213715 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = -0.819213715 + 0.9333333335 x = -0.819213715 + 0.9333333335 Combine like terms: -0.819213715 + 0.9333333335 = 0.1141196185 x = 0.1141196185 Simplifying x = 0.1141196185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7525470485, 0.1141196185}
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