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Simplifying 100x2 + -21x = 110 Reorder the terms: -21x + 100x2 = 110 Solving -21x + 100x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -21x + 100x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -21x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -1.1 + -0.21x + x2 = 0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + -0.21x + 1.1 + x2 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + -0.21x + x2 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + -0.21x + x2 = 0 + 1.1 -0.21x + x2 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 -0.21x + x2 = 1.1 The x term is -0.21x. Take half its coefficient (-0.105). Square it (0.011025) and add it to both sides. Add '0.011025' to each side of the equation. -0.21x + 0.011025 + x2 = 1.1 + 0.011025 Reorder the terms: 0.011025 + -0.21x + x2 = 1.1 + 0.011025 Combine like terms: 1.1 + 0.011025 = 1.111025 0.011025 + -0.21x + x2 = 1.111025 Factor a perfect square on the left side: (x + -0.105)(x + -0.105) = 1.111025 Calculate the square root of the right side: 1.054051707 Break this problem into two subproblems by setting (x + -0.105) equal to 1.054051707 and -1.054051707.Subproblem 1
x + -0.105 = 1.054051707 Simplifying x + -0.105 = 1.054051707 Reorder the terms: -0.105 + x = 1.054051707 Solving -0.105 + x = 1.054051707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.105' to each side of the equation. -0.105 + 0.105 + x = 1.054051707 + 0.105 Combine like terms: -0.105 + 0.105 = 0.000 0.000 + x = 1.054051707 + 0.105 x = 1.054051707 + 0.105 Combine like terms: 1.054051707 + 0.105 = 1.159051707 x = 1.159051707 Simplifying x = 1.159051707Subproblem 2
x + -0.105 = -1.054051707 Simplifying x + -0.105 = -1.054051707 Reorder the terms: -0.105 + x = -1.054051707 Solving -0.105 + x = -1.054051707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.105' to each side of the equation. -0.105 + 0.105 + x = -1.054051707 + 0.105 Combine like terms: -0.105 + 0.105 = 0.000 0.000 + x = -1.054051707 + 0.105 x = -1.054051707 + 0.105 Combine like terms: -1.054051707 + 0.105 = -0.949051707 x = -0.949051707 Simplifying x = -0.949051707Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.159051707, -0.949051707}
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