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Simplifying x2 + 19x + -142 = 0 Reorder the terms: -142 + 19x + x2 = 0 Solving -142 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 19x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 19x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 19x + x2 = 0 + 142 19x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 19x + x2 = 142 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 = 142 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 142 + 90.25 Combine like terms: 142 + 90.25 = 232.25 90.25 + 19x + x2 = 232.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 232.25 Calculate the square root of the right side: 15.239750654 Break this problem into two subproblems by setting (x + 9.5) equal to 15.239750654 and -15.239750654.Subproblem 1
x + 9.5 = 15.239750654 Simplifying x + 9.5 = 15.239750654 Reorder the terms: 9.5 + x = 15.239750654 Solving 9.5 + x = 15.239750654 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 = 15.239750654 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 15.239750654 + -9.5 x = 15.239750654 + -9.5 Combine like terms: 15.239750654 + -9.5 = 5.739750654 x = 5.739750654 Simplifying x = 5.739750654Subproblem 2
x + 9.5 = -15.239750654 Simplifying x + 9.5 = -15.239750654 Reorder the terms: 9.5 + x = -15.239750654 Solving 9.5 + x = -15.239750654 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 = -15.239750654 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -15.239750654 + -9.5 x = -15.239750654 + -9.5 Combine like terms: -15.239750654 + -9.5 = -24.739750654 x = -24.739750654 Simplifying x = -24.739750654Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.739750654, -24.739750654}
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