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Simplifying 6x2 + -15x + -14 = 0 Reorder the terms: -14 + -15x + 6x2 = 0 Solving -14 + -15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.333333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -2.5x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -2.5x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 2.333333333 -2.5x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -2.5x + x2 = 2.333333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 2.333333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 2.333333333 + 1.5625 Combine like terms: 2.333333333 + 1.5625 = 3.895833333 1.5625 + -2.5x + x2 = 3.895833333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 3.895833333 Calculate the square root of the right side: 1.973786547 Break this problem into two subproblems by setting (x + -1.25) equal to 1.973786547 and -1.973786547.Subproblem 1
x + -1.25 = 1.973786547 Simplifying x + -1.25 = 1.973786547 Reorder the terms: -1.25 + x = 1.973786547 Solving -1.25 + x = 1.973786547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.973786547 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.973786547 + 1.25 x = 1.973786547 + 1.25 Combine like terms: 1.973786547 + 1.25 = 3.223786547 x = 3.223786547 Simplifying x = 3.223786547Subproblem 2
x + -1.25 = -1.973786547 Simplifying x + -1.25 = -1.973786547 Reorder the terms: -1.25 + x = -1.973786547 Solving -1.25 + x = -1.973786547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.973786547 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.973786547 + 1.25 x = -1.973786547 + 1.25 Combine like terms: -1.973786547 + 1.25 = -0.723786547 x = -0.723786547 Simplifying x = -0.723786547Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.223786547, -0.723786547}
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