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Simplifying 10x2 + 21x + 6 = 0 Reorder the terms: 6 + 21x + 10x2 = 0 Solving 6 + 21x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.6 + 2.1x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 2.1x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 2.1x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 2.1x + x2 = 0 + -0.6 2.1x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 2.1x + x2 = -0.6 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 = -0.6 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = -0.6 + 1.1025 Combine like terms: -0.6 + 1.1025 = 0.5025 1.1025 + 2.1x + x2 = 0.5025 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + 1.05) equal to 0.708872344 and -0.708872344.Subproblem 1
x + 1.05 = 0.708872344 Simplifying x + 1.05 = 0.708872344 Reorder the terms: 1.05 + x = 0.708872344 Solving 1.05 + x = 0.708872344 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 = 0.708872344 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = 0.708872344 + -1.05 x = 0.708872344 + -1.05 Combine like terms: 0.708872344 + -1.05 = -0.341127656 x = -0.341127656 Simplifying x = -0.341127656Subproblem 2
x + 1.05 = -0.708872344 Simplifying x + 1.05 = -0.708872344 Reorder the terms: 1.05 + x = -0.708872344 Solving 1.05 + x = -0.708872344 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 = -0.708872344 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = -0.708872344 + -1.05 x = -0.708872344 + -1.05 Combine like terms: -0.708872344 + -1.05 = -1.758872344 x = -1.758872344 Simplifying x = -1.758872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.341127656, -1.758872344}
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