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Simplifying 50x2 + 63x + -7 = 0 Reorder the terms: -7 + 63x + 50x2 = 0 Solving -7 + 63x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.14 + 1.26x + x2 = 0 Move the constant term to the right: Add '0.14' to each side of the equation. -0.14 + 1.26x + 0.14 + x2 = 0 + 0.14 Reorder the terms: -0.14 + 0.14 + 1.26x + x2 = 0 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + 1.26x + x2 = 0 + 0.14 1.26x + x2 = 0 + 0.14 Combine like terms: 0 + 0.14 = 0.14 1.26x + x2 = 0.14 The x term is 1.26x. Take half its coefficient (0.63). Square it (0.3969) and add it to both sides. Add '0.3969' to each side of the equation. 1.26x + 0.3969 + x2 = 0.14 + 0.3969 Reorder the terms: 0.3969 + 1.26x + x2 = 0.14 + 0.3969 Combine like terms: 0.14 + 0.3969 = 0.5369 0.3969 + 1.26x + x2 = 0.5369 Factor a perfect square on the left side: (x + 0.63)(x + 0.63) = 0.5369 Calculate the square root of the right side: 0.732734604 Break this problem into two subproblems by setting (x + 0.63) equal to 0.732734604 and -0.732734604.Subproblem 1
x + 0.63 = 0.732734604 Simplifying x + 0.63 = 0.732734604 Reorder the terms: 0.63 + x = 0.732734604 Solving 0.63 + x = 0.732734604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63' to each side of the equation. 0.63 + -0.63 + x = 0.732734604 + -0.63 Combine like terms: 0.63 + -0.63 = 0.00 0.00 + x = 0.732734604 + -0.63 x = 0.732734604 + -0.63 Combine like terms: 0.732734604 + -0.63 = 0.102734604 x = 0.102734604 Simplifying x = 0.102734604Subproblem 2
x + 0.63 = -0.732734604 Simplifying x + 0.63 = -0.732734604 Reorder the terms: 0.63 + x = -0.732734604 Solving 0.63 + x = -0.732734604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63' to each side of the equation. 0.63 + -0.63 + x = -0.732734604 + -0.63 Combine like terms: 0.63 + -0.63 = 0.00 0.00 + x = -0.732734604 + -0.63 x = -0.732734604 + -0.63 Combine like terms: -0.732734604 + -0.63 = -1.362734604 x = -1.362734604 Simplifying x = -1.362734604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.102734604, -1.362734604}
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