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Simplifying x2 + 19x + 56 = 0 Reorder the terms: 56 + 19x + x2 = 0 Solving 56 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 19x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 19x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 19x + x2 = 0 + -56 19x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 19x + x2 = -56 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 = -56 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -56 + 90.25 Combine like terms: -56 + 90.25 = 34.25 90.25 + 19x + x2 = 34.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + 9.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + 9.5 = 5.852349955 Simplifying x + 9.5 = 5.852349955 Reorder the terms: 9.5 + x = 5.852349955 Solving 9.5 + x = 5.852349955 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 = 5.852349955 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 5.852349955 + -9.5 x = 5.852349955 + -9.5 Combine like terms: 5.852349955 + -9.5 = -3.647650045 x = -3.647650045 Simplifying x = -3.647650045Subproblem 2
x + 9.5 = -5.852349955 Simplifying x + 9.5 = -5.852349955 Reorder the terms: 9.5 + x = -5.852349955 Solving 9.5 + x = -5.852349955 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 = -5.852349955 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -5.852349955 + -9.5 x = -5.852349955 + -9.5 Combine like terms: -5.852349955 + -9.5 = -15.352349955 x = -15.352349955 Simplifying x = -15.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.647650045, -15.352349955}
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