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Simplifying 10x2 + 21x = 9 Reorder the terms: 21x + 10x2 = 9 Solving 21x + 10x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 21x + 10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 21x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 2.1x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 2.1x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 2.1x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 2.1x + x2 = 0 + 0.9 2.1x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 2.1x + x2 = 0.9 The x term is 2.1x. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1x + 1.1025 + x2 = 0.9 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = 0.9 + 1.1025 Combine like terms: 0.9 + 1.1025 = 2.0025 1.1025 + 2.1x + x2 = 2.0025 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (x + 1.05) equal to 1.41509717 and -1.41509717.Subproblem 1
x + 1.05 = 1.41509717 Simplifying x + 1.05 = 1.41509717 Reorder the terms: 1.05 + x = 1.41509717 Solving 1.05 + x = 1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = 1.41509717 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = 1.41509717 + -1.05 x = 1.41509717 + -1.05 Combine like terms: 1.41509717 + -1.05 = 0.36509717 x = 0.36509717 Simplifying x = 0.36509717Subproblem 2
x + 1.05 = -1.41509717 Simplifying x + 1.05 = -1.41509717 Reorder the terms: 1.05 + x = -1.41509717 Solving 1.05 + x = -1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = -1.41509717 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = -1.41509717 + -1.05 x = -1.41509717 + -1.05 Combine like terms: -1.41509717 + -1.05 = -2.46509717 x = -2.46509717 Simplifying x = -2.46509717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.36509717, -2.46509717}
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