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Simplifying 0 = -10 + 10x + -0.2x2 Solving 0 = -10 + 10x + -0.2x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -10x + 0.2x2 = -10 + 10x + -0.2x2 + 10 + -10x + 0.2x2 Reorder the terms: 10 + -10x + 0.2x2 = -10 + 10 + 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: -10 + 10 = 0 10 + -10x + 0.2x2 = 0 + 10x + -10x + -0.2x2 + 0.2x2 10 + -10x + 0.2x2 = 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: 10x + -10x = 0 10 + -10x + 0.2x2 = 0 + -0.2x2 + 0.2x2 10 + -10x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 10 + -10x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 50 + -50x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -50x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -50x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -50x + x2 = 0 + -50 -50x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -50x + x2 = -50 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -50 + 625 Reorder the terms: 625 + -50x + x2 = -50 + 625 Combine like terms: -50 + 625 = 575 625 + -50x + x2 = 575 Factor a perfect square on the left side: (x + -25)(x + -25) = 575 Calculate the square root of the right side: 23.979157617 Break this problem into two subproblems by setting (x + -25) equal to 23.979157617 and -23.979157617.Subproblem 1
x + -25 = 23.979157617 Simplifying x + -25 = 23.979157617 Reorder the terms: -25 + x = 23.979157617 Solving -25 + x = 23.979157617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = 23.979157617 + 25 x = 23.979157617 + 25 Combine like terms: 23.979157617 + 25 = 48.979157617 x = 48.979157617 Simplifying x = 48.979157617Subproblem 2
x + -25 = -23.979157617 Simplifying x + -25 = -23.979157617 Reorder the terms: -25 + x = -23.979157617 Solving -25 + x = -23.979157617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = -23.979157617 + 25 x = -23.979157617 + 25 Combine like terms: -23.979157617 + 25 = 1.020842383 x = 1.020842383 Simplifying x = 1.020842383Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.979157617, 1.020842383}
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