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Simplifying 7.65x2 + 2.77x = 5.38 Reorder the terms: 2.77x + 7.65x2 = 5.38 Solving 2.77x + 7.65x2 = 5.38 Solving for variable 'x'. Reorder the terms: -5.38 + 2.77x + 7.65x2 = 5.38 + -5.38 Combine like terms: 5.38 + -5.38 = 0.00 -5.38 + 2.77x + 7.65x2 = 0.00 Begin completing the square. Divide all terms by 7.65 the coefficient of the squared term: Divide each side by '7.65'. -0.7032679739 + 0.3620915033x + x2 = 0 Move the constant term to the right: Add '0.7032679739' to each side of the equation. -0.7032679739 + 0.3620915033x + 0.7032679739 + x2 = 0 + 0.7032679739 Reorder the terms: -0.7032679739 + 0.7032679739 + 0.3620915033x + x2 = 0 + 0.7032679739 Combine like terms: -0.7032679739 + 0.7032679739 = 0.0000000000 0.0000000000 + 0.3620915033x + x2 = 0 + 0.7032679739 0.3620915033x + x2 = 0 + 0.7032679739 Combine like terms: 0 + 0.7032679739 = 0.7032679739 0.3620915033x + x2 = 0.7032679739 The x term is 0.3620915033x. Take half its coefficient (0.1810457517). Square it (0.03277756421) and add it to both sides. Add '0.03277756421' to each side of the equation. 0.3620915033x + 0.03277756421 + x2 = 0.7032679739 + 0.03277756421 Reorder the terms: 0.03277756421 + 0.3620915033x + x2 = 0.7032679739 + 0.03277756421 Combine like terms: 0.7032679739 + 0.03277756421 = 0.73604553811 0.03277756421 + 0.3620915033x + x2 = 0.73604553811 Factor a perfect square on the left side: (x + 0.1810457517)(x + 0.1810457517) = 0.73604553811 Calculate the square root of the right side: 0.857930963 Break this problem into two subproblems by setting (x + 0.1810457517) equal to 0.857930963 and -0.857930963.Subproblem 1
x + 0.1810457517 = 0.857930963 Simplifying x + 0.1810457517 = 0.857930963 Reorder the terms: 0.1810457517 + x = 0.857930963 Solving 0.1810457517 + x = 0.857930963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1810457517' to each side of the equation. 0.1810457517 + -0.1810457517 + x = 0.857930963 + -0.1810457517 Combine like terms: 0.1810457517 + -0.1810457517 = 0.0000000000 0.0000000000 + x = 0.857930963 + -0.1810457517 x = 0.857930963 + -0.1810457517 Combine like terms: 0.857930963 + -0.1810457517 = 0.6768852113 x = 0.6768852113 Simplifying x = 0.6768852113Subproblem 2
x + 0.1810457517 = -0.857930963 Simplifying x + 0.1810457517 = -0.857930963 Reorder the terms: 0.1810457517 + x = -0.857930963 Solving 0.1810457517 + x = -0.857930963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1810457517' to each side of the equation. 0.1810457517 + -0.1810457517 + x = -0.857930963 + -0.1810457517 Combine like terms: 0.1810457517 + -0.1810457517 = 0.0000000000 0.0000000000 + x = -0.857930963 + -0.1810457517 x = -0.857930963 + -0.1810457517 Combine like terms: -0.857930963 + -0.1810457517 = -1.0389767147 x = -1.0389767147 Simplifying x = -1.0389767147Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6768852113, -1.0389767147}
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