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Simplifying 10x2 + 100x + 6 = 5 Reorder the terms: 6 + 100x + 10x2 = 5 Solving 6 + 100x + 10x2 = 5 Solving for variable 'x'. Reorder the terms: 6 + -5 + 100x + 10x2 = 5 + -5 Combine like terms: 6 + -5 = 1 1 + 100x + 10x2 = 5 + -5 Combine like terms: 5 + -5 = 0 1 + 100x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 10x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 10x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 10x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 10x + x2 = 0 + -0.1 10x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 10x + x2 = -0.1 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -0.1 + 25 Reorder the terms: 25 + 10x + x2 = -0.1 + 25 Combine like terms: -0.1 + 25 = 24.9 25 + 10x + x2 = 24.9 Factor a perfect square on the left side: (x + 5)(x + 5) = 24.9 Calculate the square root of the right side: 4.98998998 Break this problem into two subproblems by setting (x + 5) equal to 4.98998998 and -4.98998998.Subproblem 1
x + 5 = 4.98998998 Simplifying x + 5 = 4.98998998 Reorder the terms: 5 + x = 4.98998998 Solving 5 + x = 4.98998998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.98998998 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.98998998 + -5 x = 4.98998998 + -5 Combine like terms: 4.98998998 + -5 = -0.01001002 x = -0.01001002 Simplifying x = -0.01001002Subproblem 2
x + 5 = -4.98998998 Simplifying x + 5 = -4.98998998 Reorder the terms: 5 + x = -4.98998998 Solving 5 + x = -4.98998998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.98998998 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.98998998 + -5 x = -4.98998998 + -5 Combine like terms: -4.98998998 + -5 = -9.98998998 x = -9.98998998 Simplifying x = -9.98998998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.01001002, -9.98998998}
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