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Simplifying -5x2 + -7 + 6x + 14x2 + -12x = 0 Reorder the terms: -7 + 6x + -12x + -5x2 + 14x2 = 0 Combine like terms: 6x + -12x = -6x -7 + -6x + -5x2 + 14x2 = 0 Combine like terms: -5x2 + 14x2 = 9x2 -7 + -6x + 9x2 = 0 Solving -7 + -6x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -0.6666666667x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + 0.7777777778 -0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -0.6666666667x + x2 = 0.7777777778 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.7777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.7777777778 + 0.1111111112 Combine like terms: 0.7777777778 + 0.1111111112 = 0.888888889 0.1111111112 + -0.6666666667x + x2 = 0.888888889 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.888888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.942809042 and -0.942809042.Subproblem 1
x + -0.3333333334 = 0.942809042 Simplifying x + -0.3333333334 = 0.942809042 Reorder the terms: -0.3333333334 + x = 0.942809042 Solving -0.3333333334 + x = 0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.942809042 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.942809042 + 0.3333333334 x = 0.942809042 + 0.3333333334 Combine like terms: 0.942809042 + 0.3333333334 = 1.2761423754 x = 1.2761423754 Simplifying x = 1.2761423754Subproblem 2
x + -0.3333333334 = -0.942809042 Simplifying x + -0.3333333334 = -0.942809042 Reorder the terms: -0.3333333334 + x = -0.942809042 Solving -0.3333333334 + x = -0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.942809042 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.942809042 + 0.3333333334 x = -0.942809042 + 0.3333333334 Combine like terms: -0.942809042 + 0.3333333334 = -0.6094757086 x = -0.6094757086 Simplifying x = -0.6094757086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2761423754, -0.6094757086}
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