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Simplifying x(15x + -28) = 12 Reorder the terms: x(-28 + 15x) = 12 (-28 * x + 15x * x) = 12 (-28x + 15x2) = 12 Solving -28x + 15x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -28x + 15x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -28x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + -1.866666667x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.866666667x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.866666667x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.866666667x + x2 = 0 + 0.8 -1.866666667x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.866666667x + x2 = 0.8 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 = 0.8 + 0.8711111114 Reorder the terms: 0.8711111114 + -1.866666667x + x2 = 0.8 + 0.8711111114 Combine like terms: 0.8 + 0.8711111114 = 1.6711111114 0.8711111114 + -1.866666667x + x2 = 1.6711111114 Factor a perfect square on the left side: (x + -0.9333333335)(x + -0.9333333335) = 1.6711111114 Calculate the square root of the right side: 1.292714629 Break this problem into two subproblems by setting (x + -0.9333333335) equal to 1.292714629 and -1.292714629.Subproblem 1
x + -0.9333333335 = 1.292714629 Simplifying x + -0.9333333335 = 1.292714629 Reorder the terms: -0.9333333335 + x = 1.292714629 Solving -0.9333333335 + x = 1.292714629 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 = 1.292714629 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = 1.292714629 + 0.9333333335 x = 1.292714629 + 0.9333333335 Combine like terms: 1.292714629 + 0.9333333335 = 2.2260479625 x = 2.2260479625 Simplifying x = 2.2260479625Subproblem 2
x + -0.9333333335 = -1.292714629 Simplifying x + -0.9333333335 = -1.292714629 Reorder the terms: -0.9333333335 + x = -1.292714629 Solving -0.9333333335 + x = -1.292714629 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 = -1.292714629 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = -1.292714629 + 0.9333333335 x = -1.292714629 + 0.9333333335 Combine like terms: -1.292714629 + 0.9333333335 = -0.3593812955 x = -0.3593812955 Simplifying x = -0.3593812955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2260479625, -0.3593812955}
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