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Simplifying 5x2 + -2 + -14x2 + 9 + 8x = 0 Reorder the terms: -2 + 9 + 8x + 5x2 + -14x2 = 0 Combine like terms: -2 + 9 = 7 7 + 8x + 5x2 + -14x2 = 0 Combine like terms: 5x2 + -14x2 = -9x2 7 + 8x + -9x2 = 0 Solving 7 + 8x + -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 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -0.8888888889x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -0.8888888889x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.7777777778 -0.8888888889x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -0.8888888889x + x2 = 0.7777777778 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.7777777778 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.7777777778 + 0.1975308642 Combine like terms: 0.7777777778 + 0.1975308642 = 0.975308642 0.1975308642 + -0.8888888889x + x2 = 0.975308642 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.975308642 Calculate the square root of the right side: 0.987577157 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.987577157 and -0.987577157.Subproblem 1
x + -0.4444444445 = 0.987577157 Simplifying x + -0.4444444445 = 0.987577157 Reorder the terms: -0.4444444445 + x = 0.987577157 Solving -0.4444444445 + x = 0.987577157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.987577157 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.987577157 + 0.4444444445 x = 0.987577157 + 0.4444444445 Combine like terms: 0.987577157 + 0.4444444445 = 1.4320216015 x = 1.4320216015 Simplifying x = 1.4320216015Subproblem 2
x + -0.4444444445 = -0.987577157 Simplifying x + -0.4444444445 = -0.987577157 Reorder the terms: -0.4444444445 + x = -0.987577157 Solving -0.4444444445 + x = -0.987577157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.987577157 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.987577157 + 0.4444444445 x = -0.987577157 + 0.4444444445 Combine like terms: -0.987577157 + 0.4444444445 = -0.5431327125 x = -0.5431327125 Simplifying x = -0.5431327125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4320216015, -0.5431327125}
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