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Simplifying 0 = -4.9x2 + 5x + 1 Reorder the terms: 0 = 1 + 5x + -4.9x2 Solving 0 = 1 + 5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -5x + 4.9x2 = 1 + 5x + -4.9x2 + -1 + -5x + 4.9x2 Reorder the terms: -1 + -5x + 4.9x2 = 1 + -1 + 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 1 + -1 = 0 -1 + -5x + 4.9x2 = 0 + 5x + -5x + -4.9x2 + 4.9x2 -1 + -5x + 4.9x2 = 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 5x + -5x = 0 -1 + -5x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -1 + -5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1 + -5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2040816327 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -1.020408163x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -1.020408163x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -1.020408163x + x2 = 0 + 0.2040816327 -1.020408163x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -1.020408163x + x2 = 0.2040816327 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 0.2040816327 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 0.2040816327 + 0.2603082048 Combine like terms: 0.2040816327 + 0.2603082048 = 0.4643898375 0.2603082048 + -1.020408163x + x2 = 0.4643898375 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 0.4643898375 Calculate the square root of the right side: 0.681461545 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 0.681461545 and -0.681461545.Subproblem 1
x + -0.5102040815 = 0.681461545 Simplifying x + -0.5102040815 = 0.681461545 Reorder the terms: -0.5102040815 + x = 0.681461545 Solving -0.5102040815 + x = 0.681461545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 0.681461545 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 0.681461545 + 0.5102040815 x = 0.681461545 + 0.5102040815 Combine like terms: 0.681461545 + 0.5102040815 = 1.1916656265 x = 1.1916656265 Simplifying x = 1.1916656265Subproblem 2
x + -0.5102040815 = -0.681461545 Simplifying x + -0.5102040815 = -0.681461545 Reorder the terms: -0.5102040815 + x = -0.681461545 Solving -0.5102040815 + x = -0.681461545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -0.681461545 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -0.681461545 + 0.5102040815 x = -0.681461545 + 0.5102040815 Combine like terms: -0.681461545 + 0.5102040815 = -0.1712574635 x = -0.1712574635 Simplifying x = -0.1712574635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1916656265, -0.1712574635}
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