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Simplifying 0 = -0.1x2 + 34x + 10 Reorder the terms: 0 = 10 + 34x + -0.1x2 Solving 0 = 10 + 34x + -0.1x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -34x + 0.1x2 = 10 + 34x + -0.1x2 + -10 + -34x + 0.1x2 Reorder the terms: -10 + -34x + 0.1x2 = 10 + -10 + 34x + -34x + -0.1x2 + 0.1x2 Combine like terms: 10 + -10 = 0 -10 + -34x + 0.1x2 = 0 + 34x + -34x + -0.1x2 + 0.1x2 -10 + -34x + 0.1x2 = 34x + -34x + -0.1x2 + 0.1x2 Combine like terms: 34x + -34x = 0 -10 + -34x + 0.1x2 = 0 + -0.1x2 + 0.1x2 -10 + -34x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -10 + -34x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -100 + -340x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -340x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -340x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -340x + x2 = 0 + 100 -340x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -340x + x2 = 100 The x term is -340x. Take half its coefficient (-170). Square it (28900) and add it to both sides. Add '28900' to each side of the equation. -340x + 28900 + x2 = 100 + 28900 Reorder the terms: 28900 + -340x + x2 = 100 + 28900 Combine like terms: 100 + 28900 = 29000 28900 + -340x + x2 = 29000 Factor a perfect square on the left side: (x + -170)(x + -170) = 29000 Calculate the square root of the right side: 170.293863659 Break this problem into two subproblems by setting (x + -170) equal to 170.293863659 and -170.293863659.Subproblem 1
x + -170 = 170.293863659 Simplifying x + -170 = 170.293863659 Reorder the terms: -170 + x = 170.293863659 Solving -170 + x = 170.293863659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170' to each side of the equation. -170 + 170 + x = 170.293863659 + 170 Combine like terms: -170 + 170 = 0 0 + x = 170.293863659 + 170 x = 170.293863659 + 170 Combine like terms: 170.293863659 + 170 = 340.293863659 x = 340.293863659 Simplifying x = 340.293863659Subproblem 2
x + -170 = -170.293863659 Simplifying x + -170 = -170.293863659 Reorder the terms: -170 + x = -170.293863659 Solving -170 + x = -170.293863659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170' to each side of the equation. -170 + 170 + x = -170.293863659 + 170 Combine like terms: -170 + 170 = 0 0 + x = -170.293863659 + 170 x = -170.293863659 + 170 Combine like terms: -170.293863659 + 170 = -0.293863659 x = -0.293863659 Simplifying x = -0.293863659Solution
The solution to the problem is based on the solutions from the subproblems. x = {340.293863659, -0.293863659}
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