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Simplifying x2 + 19x + -6 = 0 Reorder the terms: -6 + 19x + x2 = 0 Solving -6 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 19x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 19x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 19x + x2 = 0 + 6 19x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 19x + x2 = 6 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 6 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 6 + 90.25 Combine like terms: 6 + 90.25 = 96.25 90.25 + 19x + x2 = 96.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 9.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 9.5 = 9.810708435 Simplifying x + 9.5 = 9.810708435 Reorder the terms: 9.5 + x = 9.810708435 Solving 9.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.810708435 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.810708435 + -9.5 x = 9.810708435 + -9.5 Combine like terms: 9.810708435 + -9.5 = 0.310708435 x = 0.310708435 Simplifying x = 0.310708435Subproblem 2
x + 9.5 = -9.810708435 Simplifying x + 9.5 = -9.810708435 Reorder the terms: 9.5 + x = -9.810708435 Solving 9.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.810708435 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.810708435 + -9.5 x = -9.810708435 + -9.5 Combine like terms: -9.810708435 + -9.5 = -19.310708435 x = -19.310708435 Simplifying x = -19.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.310708435, -19.310708435}
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