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Simplifying x2 + 19x + 87 = 0 Reorder the terms: 87 + 19x + x2 = 0 Solving 87 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-87' to each side of the equation. 87 + 19x + -87 + x2 = 0 + -87 Reorder the terms: 87 + -87 + 19x + x2 = 0 + -87 Combine like terms: 87 + -87 = 0 0 + 19x + x2 = 0 + -87 19x + x2 = 0 + -87 Combine like terms: 0 + -87 = -87 19x + x2 = -87 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 = -87 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -87 + 90.25 Combine like terms: -87 + 90.25 = 3.25 90.25 + 19x + x2 = 3.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 9.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 9.5 = 1.802775638 Simplifying x + 9.5 = 1.802775638 Reorder the terms: 9.5 + x = 1.802775638 Solving 9.5 + x = 1.802775638 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 = 1.802775638 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 1.802775638 + -9.5 x = 1.802775638 + -9.5 Combine like terms: 1.802775638 + -9.5 = -7.697224362 x = -7.697224362 Simplifying x = -7.697224362Subproblem 2
x + 9.5 = -1.802775638 Simplifying x + 9.5 = -1.802775638 Reorder the terms: 9.5 + x = -1.802775638 Solving 9.5 + x = -1.802775638 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 = -1.802775638 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -1.802775638 + -9.5 x = -1.802775638 + -9.5 Combine like terms: -1.802775638 + -9.5 = -11.302775638 x = -11.302775638 Simplifying x = -11.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.697224362, -11.302775638}
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