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Simplifying 0 = x2 + 10x + 19 Reorder the terms: 0 = 19 + 10x + x2 Solving 0 = 19 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + -19 = -19 -19 + -10x + -1x2 = 19 + 10x + x2 + -19 + -10x + -1x2 Reorder the terms: -19 + -10x + -1x2 = 19 + -19 + 10x + -10x + x2 + -1x2 Combine like terms: 19 + -19 = 0 -19 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -19 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -19 + -10x + -1x2 = 0 + x2 + -1x2 -19 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -19 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 10x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + 10x + x2)' equal to zero and attempt to solve: Simplifying 19 + 10x + x2 = 0 Solving 19 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 10x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 10x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 10x + x2 = 0 + -19 10x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 10x + x2 = -19 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 = -19 + 25 Reorder the terms: 25 + 10x + x2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + 10x + x2 = 6 Factor a perfect square on the left side: (x + 5)(x + 5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 5 = 2.449489743 Simplifying x + 5 = 2.449489743 Reorder the terms: 5 + x = 2.449489743 Solving 5 + x = 2.449489743 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 = 2.449489743 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.449489743 + -5 x = 2.449489743 + -5 Combine like terms: 2.449489743 + -5 = -2.550510257 x = -2.550510257 Simplifying x = -2.550510257Subproblem 2
x + 5 = -2.449489743 Simplifying x + 5 = -2.449489743 Reorder the terms: 5 + x = -2.449489743 Solving 5 + x = -2.449489743 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 = -2.449489743 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.449489743 + -5 x = -2.449489743 + -5 Combine like terms: -2.449489743 + -5 = -7.449489743 x = -7.449489743 Simplifying x = -7.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.550510257, -7.449489743}Solution
x = {-2.550510257, -7.449489743}
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