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Simplifying x2 + 148x + 1896 = 0 Reorder the terms: 1896 + 148x + x2 = 0 Solving 1896 + 148x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1896' to each side of the equation. 1896 + 148x + -1896 + x2 = 0 + -1896 Reorder the terms: 1896 + -1896 + 148x + x2 = 0 + -1896 Combine like terms: 1896 + -1896 = 0 0 + 148x + x2 = 0 + -1896 148x + x2 = 0 + -1896 Combine like terms: 0 + -1896 = -1896 148x + x2 = -1896 The x term is 148x. Take half its coefficient (74). Square it (5476) and add it to both sides. Add '5476' to each side of the equation. 148x + 5476 + x2 = -1896 + 5476 Reorder the terms: 5476 + 148x + x2 = -1896 + 5476 Combine like terms: -1896 + 5476 = 3580 5476 + 148x + x2 = 3580 Factor a perfect square on the left side: (x + 74)(x + 74) = 3580 Calculate the square root of the right side: 59.833101207 Break this problem into two subproblems by setting (x + 74) equal to 59.833101207 and -59.833101207.Subproblem 1
x + 74 = 59.833101207 Simplifying x + 74 = 59.833101207 Reorder the terms: 74 + x = 59.833101207 Solving 74 + x = 59.833101207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-74' to each side of the equation. 74 + -74 + x = 59.833101207 + -74 Combine like terms: 74 + -74 = 0 0 + x = 59.833101207 + -74 x = 59.833101207 + -74 Combine like terms: 59.833101207 + -74 = -14.166898793 x = -14.166898793 Simplifying x = -14.166898793Subproblem 2
x + 74 = -59.833101207 Simplifying x + 74 = -59.833101207 Reorder the terms: 74 + x = -59.833101207 Solving 74 + x = -59.833101207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-74' to each side of the equation. 74 + -74 + x = -59.833101207 + -74 Combine like terms: 74 + -74 = 0 0 + x = -59.833101207 + -74 x = -59.833101207 + -74 Combine like terms: -59.833101207 + -74 = -133.833101207 x = -133.833101207 Simplifying x = -133.833101207Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.166898793, -133.833101207}
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