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Simplifying 0 = -0.01x2 + 0.7x + 5.8 Reorder the terms: 0 = 5.8 + 0.7x + -0.01x2 Solving 0 = 5.8 + 0.7x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -5.8 = -5.8 -5.8 + -0.7x + 0.01x2 = 5.8 + 0.7x + -0.01x2 + -5.8 + -0.7x + 0.01x2 Reorder the terms: -5.8 + -0.7x + 0.01x2 = 5.8 + -5.8 + 0.7x + -0.7x + -0.01x2 + 0.01x2 Combine like terms: 5.8 + -5.8 = 0.0 -5.8 + -0.7x + 0.01x2 = 0.0 + 0.7x + -0.7x + -0.01x2 + 0.01x2 -5.8 + -0.7x + 0.01x2 = 0.7x + -0.7x + -0.01x2 + 0.01x2 Combine like terms: 0.7x + -0.7x = 0.0 -5.8 + -0.7x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -5.8 + -0.7x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -5.8 + -0.7x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -580 + -70x + x2 = 0 Move the constant term to the right: Add '580' to each side of the equation. -580 + -70x + 580 + x2 = 0 + 580 Reorder the terms: -580 + 580 + -70x + x2 = 0 + 580 Combine like terms: -580 + 580 = 0 0 + -70x + x2 = 0 + 580 -70x + x2 = 0 + 580 Combine like terms: 0 + 580 = 580 -70x + x2 = 580 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = 580 + 1225 Reorder the terms: 1225 + -70x + x2 = 580 + 1225 Combine like terms: 580 + 1225 = 1805 1225 + -70x + x2 = 1805 Factor a perfect square on the left side: (x + -35)(x + -35) = 1805 Calculate the square root of the right side: 42.485291572 Break this problem into two subproblems by setting (x + -35) equal to 42.485291572 and -42.485291572.Subproblem 1
x + -35 = 42.485291572 Simplifying x + -35 = 42.485291572 Reorder the terms: -35 + x = 42.485291572 Solving -35 + x = 42.485291572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 42.485291572 + 35 Combine like terms: -35 + 35 = 0 0 + x = 42.485291572 + 35 x = 42.485291572 + 35 Combine like terms: 42.485291572 + 35 = 77.485291572 x = 77.485291572 Simplifying x = 77.485291572Subproblem 2
x + -35 = -42.485291572 Simplifying x + -35 = -42.485291572 Reorder the terms: -35 + x = -42.485291572 Solving -35 + x = -42.485291572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -42.485291572 + 35 Combine like terms: -35 + 35 = 0 0 + x = -42.485291572 + 35 x = -42.485291572 + 35 Combine like terms: -42.485291572 + 35 = -7.485291572 x = -7.485291572 Simplifying x = -7.485291572Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.485291572, -7.485291572}
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