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Simplifying x2 + 25x + 153 = 0 Reorder the terms: 153 + 25x + x2 = 0 Solving 153 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-153' to each side of the equation. 153 + 25x + -153 + x2 = 0 + -153 Reorder the terms: 153 + -153 + 25x + x2 = 0 + -153 Combine like terms: 153 + -153 = 0 0 + 25x + x2 = 0 + -153 25x + x2 = 0 + -153 Combine like terms: 0 + -153 = -153 25x + x2 = -153 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -153 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -153 + 156.25 Combine like terms: -153 + 156.25 = 3.25 156.25 + 25x + x2 = 3.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 12.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 12.5 = 1.802775638 Simplifying x + 12.5 = 1.802775638 Reorder the terms: 12.5 + x = 1.802775638 Solving 12.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 1.802775638 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 1.802775638 + -12.5 x = 1.802775638 + -12.5 Combine like terms: 1.802775638 + -12.5 = -10.697224362 x = -10.697224362 Simplifying x = -10.697224362Subproblem 2
x + 12.5 = -1.802775638 Simplifying x + 12.5 = -1.802775638 Reorder the terms: 12.5 + x = -1.802775638 Solving 12.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -1.802775638 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -1.802775638 + -12.5 x = -1.802775638 + -12.5 Combine like terms: -1.802775638 + -12.5 = -14.302775638 x = -14.302775638 Simplifying x = -14.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.697224362, -14.302775638}
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