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Simplifying 279x2 + 392x + -196 = 0 Reorder the terms: -196 + 392x + 279x2 = 0 Solving -196 + 392x + 279x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 279 the coefficient of the squared term: Divide each side by '279'. -0.7025089606 + 1.405017921x + x2 = 0 Move the constant term to the right: Add '0.7025089606' to each side of the equation. -0.7025089606 + 1.405017921x + 0.7025089606 + x2 = 0 + 0.7025089606 Reorder the terms: -0.7025089606 + 0.7025089606 + 1.405017921x + x2 = 0 + 0.7025089606 Combine like terms: -0.7025089606 + 0.7025089606 = 0.0000000000 0.0000000000 + 1.405017921x + x2 = 0 + 0.7025089606 1.405017921x + x2 = 0 + 0.7025089606 Combine like terms: 0 + 0.7025089606 = 0.7025089606 1.405017921x + x2 = 0.7025089606 The x term is 1.405017921x. Take half its coefficient (0.7025089605). Square it (0.4935188396) and add it to both sides. Add '0.4935188396' to each side of the equation. 1.405017921x + 0.4935188396 + x2 = 0.7025089606 + 0.4935188396 Reorder the terms: 0.4935188396 + 1.405017921x + x2 = 0.7025089606 + 0.4935188396 Combine like terms: 0.7025089606 + 0.4935188396 = 1.1960278002 0.4935188396 + 1.405017921x + x2 = 1.1960278002 Factor a perfect square on the left side: (x + 0.7025089605)(x + 0.7025089605) = 1.1960278002 Calculate the square root of the right side: 1.093630559 Break this problem into two subproblems by setting (x + 0.7025089605) equal to 1.093630559 and -1.093630559.Subproblem 1
x + 0.7025089605 = 1.093630559 Simplifying x + 0.7025089605 = 1.093630559 Reorder the terms: 0.7025089605 + x = 1.093630559 Solving 0.7025089605 + x = 1.093630559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7025089605' to each side of the equation. 0.7025089605 + -0.7025089605 + x = 1.093630559 + -0.7025089605 Combine like terms: 0.7025089605 + -0.7025089605 = 0.0000000000 0.0000000000 + x = 1.093630559 + -0.7025089605 x = 1.093630559 + -0.7025089605 Combine like terms: 1.093630559 + -0.7025089605 = 0.3911215985 x = 0.3911215985 Simplifying x = 0.3911215985Subproblem 2
x + 0.7025089605 = -1.093630559 Simplifying x + 0.7025089605 = -1.093630559 Reorder the terms: 0.7025089605 + x = -1.093630559 Solving 0.7025089605 + x = -1.093630559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7025089605' to each side of the equation. 0.7025089605 + -0.7025089605 + x = -1.093630559 + -0.7025089605 Combine like terms: 0.7025089605 + -0.7025089605 = 0.0000000000 0.0000000000 + x = -1.093630559 + -0.7025089605 x = -1.093630559 + -0.7025089605 Combine like terms: -1.093630559 + -0.7025089605 = -1.7961395195 x = -1.7961395195 Simplifying x = -1.7961395195Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3911215985, -1.7961395195}
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