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Simplifying 74x2 + 7x + -7 = 0 Reorder the terms: -7 + 7x + 74x2 = 0 Solving -7 + 7x + 74x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 74 the coefficient of the squared term: Divide each side by '74'. -0.09459459459 + 0.09459459459x + x2 = 0 Move the constant term to the right: Add '0.09459459459' to each side of the equation. -0.09459459459 + 0.09459459459x + 0.09459459459 + x2 = 0 + 0.09459459459 Reorder the terms: -0.09459459459 + 0.09459459459 + 0.09459459459x + x2 = 0 + 0.09459459459 Combine like terms: -0.09459459459 + 0.09459459459 = 0.00000000000 0.00000000000 + 0.09459459459x + x2 = 0 + 0.09459459459 0.09459459459x + x2 = 0 + 0.09459459459 Combine like terms: 0 + 0.09459459459 = 0.09459459459 0.09459459459x + x2 = 0.09459459459 The x term is 0.09459459459x. Take half its coefficient (0.0472972973). Square it (0.002237034332) and add it to both sides. Add '0.002237034332' to each side of the equation. 0.09459459459x + 0.002237034332 + x2 = 0.09459459459 + 0.002237034332 Reorder the terms: 0.002237034332 + 0.09459459459x + x2 = 0.09459459459 + 0.002237034332 Combine like terms: 0.09459459459 + 0.002237034332 = 0.096831628922 0.002237034332 + 0.09459459459x + x2 = 0.096831628922 Factor a perfect square on the left side: (x + 0.0472972973)(x + 0.0472972973) = 0.096831628922 Calculate the square root of the right side: 0.311177809 Break this problem into two subproblems by setting (x + 0.0472972973) equal to 0.311177809 and -0.311177809.Subproblem 1
x + 0.0472972973 = 0.311177809 Simplifying x + 0.0472972973 = 0.311177809 Reorder the terms: 0.0472972973 + x = 0.311177809 Solving 0.0472972973 + x = 0.311177809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0472972973' to each side of the equation. 0.0472972973 + -0.0472972973 + x = 0.311177809 + -0.0472972973 Combine like terms: 0.0472972973 + -0.0472972973 = 0.0000000000 0.0000000000 + x = 0.311177809 + -0.0472972973 x = 0.311177809 + -0.0472972973 Combine like terms: 0.311177809 + -0.0472972973 = 0.2638805117 x = 0.2638805117 Simplifying x = 0.2638805117Subproblem 2
x + 0.0472972973 = -0.311177809 Simplifying x + 0.0472972973 = -0.311177809 Reorder the terms: 0.0472972973 + x = -0.311177809 Solving 0.0472972973 + x = -0.311177809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0472972973' to each side of the equation. 0.0472972973 + -0.0472972973 + x = -0.311177809 + -0.0472972973 Combine like terms: 0.0472972973 + -0.0472972973 = 0.0000000000 0.0000000000 + x = -0.311177809 + -0.0472972973 x = -0.311177809 + -0.0472972973 Combine like terms: -0.311177809 + -0.0472972973 = -0.3584751063 x = -0.3584751063 Simplifying x = -0.3584751063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2638805117, -0.3584751063}
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