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Simplifying 0 = 0.01x2 + 0.7x + 6.1 Reorder the terms: 0 = 6.1 + 0.7x + 0.01x2 Solving 0 = 6.1 + 0.7x + 0.01x2 Solving for variable 'x'. Combine like terms: 0 + -6.1 = -6.1 -6.1 + -0.7x + -0.01x2 = 6.1 + 0.7x + 0.01x2 + -6.1 + -0.7x + -0.01x2 Reorder the terms: -6.1 + -0.7x + -0.01x2 = 6.1 + -6.1 + 0.7x + -0.7x + 0.01x2 + -0.01x2 Combine like terms: 6.1 + -6.1 = 0.0 -6.1 + -0.7x + -0.01x2 = 0.0 + 0.7x + -0.7x + 0.01x2 + -0.01x2 -6.1 + -0.7x + -0.01x2 = 0.7x + -0.7x + 0.01x2 + -0.01x2 Combine like terms: 0.7x + -0.7x = 0.0 -6.1 + -0.7x + -0.01x2 = 0.0 + 0.01x2 + -0.01x2 -6.1 + -0.7x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -6.1 + -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'. 610 + 70x + x2 = 0 Move the constant term to the right: Add '-610' to each side of the equation. 610 + 70x + -610 + x2 = 0 + -610 Reorder the terms: 610 + -610 + 70x + x2 = 0 + -610 Combine like terms: 610 + -610 = 0 0 + 70x + x2 = 0 + -610 70x + x2 = 0 + -610 Combine like terms: 0 + -610 = -610 70x + x2 = -610 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 = -610 + 1225 Reorder the terms: 1225 + 70x + x2 = -610 + 1225 Combine like terms: -610 + 1225 = 615 1225 + 70x + x2 = 615 Factor a perfect square on the left side: (x + 35)(x + 35) = 615 Calculate the square root of the right side: 24.799193535 Break this problem into two subproblems by setting (x + 35) equal to 24.799193535 and -24.799193535.Subproblem 1
x + 35 = 24.799193535 Simplifying x + 35 = 24.799193535 Reorder the terms: 35 + x = 24.799193535 Solving 35 + x = 24.799193535 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 = 24.799193535 + -35 Combine like terms: 35 + -35 = 0 0 + x = 24.799193535 + -35 x = 24.799193535 + -35 Combine like terms: 24.799193535 + -35 = -10.200806465 x = -10.200806465 Simplifying x = -10.200806465Subproblem 2
x + 35 = -24.799193535 Simplifying x + 35 = -24.799193535 Reorder the terms: 35 + x = -24.799193535 Solving 35 + x = -24.799193535 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 = -24.799193535 + -35 Combine like terms: 35 + -35 = 0 0 + x = -24.799193535 + -35 x = -24.799193535 + -35 Combine like terms: -24.799193535 + -35 = -59.799193535 x = -59.799193535 Simplifying x = -59.799193535Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.200806465, -59.799193535}
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