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Simplifying 0 = x2 + 10x + 1 Reorder the terms: 0 = 1 + 10x + x2 Solving 0 = 1 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -10x + -1x2 = 1 + 10x + x2 + -1 + -10x + -1x2 Reorder the terms: -1 + -10x + -1x2 = 1 + -1 + 10x + -10x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -1 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -1 + -10x + -1x2 = 0 + x2 + -1x2 -1 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 10x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 10x + x2)' equal to zero and attempt to solve: Simplifying 1 + 10x + x2 = 0 Solving 1 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 10x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 10x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10x + x2 = 0 + -1 10x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 10x + x2 = -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 = -1 + 25 Reorder the terms: 25 + 10x + x2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + 10x + x2 = 24 Factor a perfect square on the left side: (x + 5)(x + 5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 5) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 5 = 4.898979486 Simplifying x + 5 = 4.898979486 Reorder the terms: 5 + x = 4.898979486 Solving 5 + x = 4.898979486 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 = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.898979486 + -5 x = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 x = -0.101020514 Simplifying x = -0.101020514Subproblem 2
x + 5 = -4.898979486 Simplifying x + 5 = -4.898979486 Reorder the terms: 5 + x = -4.898979486 Solving 5 + x = -4.898979486 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 = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.898979486 + -5 x = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 x = -9.898979486 Simplifying x = -9.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.101020514, -9.898979486}Solution
x = {-0.101020514, -9.898979486}
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