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Simplifying 7.61x2 + 2.72x = 5.32 Reorder the terms: 2.72x + 7.61x2 = 5.32 Solving 2.72x + 7.61x2 = 5.32 Solving for variable 'x'. Reorder the terms: -5.32 + 2.72x + 7.61x2 = 5.32 + -5.32 Combine like terms: 5.32 + -5.32 = 0.00 -5.32 + 2.72x + 7.61x2 = 0.00 Begin completing the square. Divide all terms by 7.61 the coefficient of the squared term: Divide each side by '7.61'. -0.6990801577 + 0.3574244415x + x2 = 0 Move the constant term to the right: Add '0.6990801577' to each side of the equation. -0.6990801577 + 0.3574244415x + 0.6990801577 + x2 = 0 + 0.6990801577 Reorder the terms: -0.6990801577 + 0.6990801577 + 0.3574244415x + x2 = 0 + 0.6990801577 Combine like terms: -0.6990801577 + 0.6990801577 = 0.0000000000 0.0000000000 + 0.3574244415x + x2 = 0 + 0.6990801577 0.3574244415x + x2 = 0 + 0.6990801577 Combine like terms: 0 + 0.6990801577 = 0.6990801577 0.3574244415x + x2 = 0.6990801577 The x term is 0.3574244415x. Take half its coefficient (0.1787122208). Square it (0.03193805786) and add it to both sides. Add '0.03193805786' to each side of the equation. 0.3574244415x + 0.03193805786 + x2 = 0.6990801577 + 0.03193805786 Reorder the terms: 0.03193805786 + 0.3574244415x + x2 = 0.6990801577 + 0.03193805786 Combine like terms: 0.6990801577 + 0.03193805786 = 0.73101821556 0.03193805786 + 0.3574244415x + x2 = 0.73101821556 Factor a perfect square on the left side: (x + 0.1787122208)(x + 0.1787122208) = 0.73101821556 Calculate the square root of the right side: 0.854996032 Break this problem into two subproblems by setting (x + 0.1787122208) equal to 0.854996032 and -0.854996032.Subproblem 1
x + 0.1787122208 = 0.854996032 Simplifying x + 0.1787122208 = 0.854996032 Reorder the terms: 0.1787122208 + x = 0.854996032 Solving 0.1787122208 + x = 0.854996032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1787122208' to each side of the equation. 0.1787122208 + -0.1787122208 + x = 0.854996032 + -0.1787122208 Combine like terms: 0.1787122208 + -0.1787122208 = 0.0000000000 0.0000000000 + x = 0.854996032 + -0.1787122208 x = 0.854996032 + -0.1787122208 Combine like terms: 0.854996032 + -0.1787122208 = 0.6762838112 x = 0.6762838112 Simplifying x = 0.6762838112Subproblem 2
x + 0.1787122208 = -0.854996032 Simplifying x + 0.1787122208 = -0.854996032 Reorder the terms: 0.1787122208 + x = -0.854996032 Solving 0.1787122208 + x = -0.854996032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1787122208' to each side of the equation. 0.1787122208 + -0.1787122208 + x = -0.854996032 + -0.1787122208 Combine like terms: 0.1787122208 + -0.1787122208 = 0.0000000000 0.0000000000 + x = -0.854996032 + -0.1787122208 x = -0.854996032 + -0.1787122208 Combine like terms: -0.854996032 + -0.1787122208 = -1.0337082528 x = -1.0337082528 Simplifying x = -1.0337082528Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6762838112, -1.0337082528}
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