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Simplifying 0.0000852x2 + -0.0122x + 0.0514 = 0 Reorder the terms: 0.0514 + -0.0122x + 0.0000852x2 = 0 Solving 0.0514 + -0.0122x + 0.0000852x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000852 the coefficient of the squared term: Divide each side by '0.0000852'. 603.286385 + -143.1924883x + x2 = 0 Move the constant term to the right: Add '-603.286385' to each side of the equation. 603.286385 + -143.1924883x + -603.286385 + x2 = 0 + -603.286385 Reorder the terms: 603.286385 + -603.286385 + -143.1924883x + x2 = 0 + -603.286385 Combine like terms: 603.286385 + -603.286385 = 0.000000 0.000000 + -143.1924883x + x2 = 0 + -603.286385 -143.1924883x + x2 = 0 + -603.286385 Combine like terms: 0 + -603.286385 = -603.286385 -143.1924883x + x2 = -603.286385 The x term is -143.1924883x. Take half its coefficient (-71.59624415). Square it (5126.022176) and add it to both sides. Add '5126.022176' to each side of the equation. -143.1924883x + 5126.022176 + x2 = -603.286385 + 5126.022176 Reorder the terms: 5126.022176 + -143.1924883x + x2 = -603.286385 + 5126.022176 Combine like terms: -603.286385 + 5126.022176 = 4522.735791 5126.022176 + -143.1924883x + x2 = 4522.735791 Factor a perfect square on the left side: (x + -71.59624415)(x + -71.59624415) = 4522.735791 Calculate the square root of the right side: 67.251288397 Break this problem into two subproblems by setting (x + -71.59624415) equal to 67.251288397 and -67.251288397.Subproblem 1
x + -71.59624415 = 67.251288397 Simplifying x + -71.59624415 = 67.251288397 Reorder the terms: -71.59624415 + x = 67.251288397 Solving -71.59624415 + x = 67.251288397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.59624415' to each side of the equation. -71.59624415 + 71.59624415 + x = 67.251288397 + 71.59624415 Combine like terms: -71.59624415 + 71.59624415 = 0.00000000 0.00000000 + x = 67.251288397 + 71.59624415 x = 67.251288397 + 71.59624415 Combine like terms: 67.251288397 + 71.59624415 = 138.847532547 x = 138.847532547 Simplifying x = 138.847532547Subproblem 2
x + -71.59624415 = -67.251288397 Simplifying x + -71.59624415 = -67.251288397 Reorder the terms: -71.59624415 + x = -67.251288397 Solving -71.59624415 + x = -67.251288397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.59624415' to each side of the equation. -71.59624415 + 71.59624415 + x = -67.251288397 + 71.59624415 Combine like terms: -71.59624415 + 71.59624415 = 0.00000000 0.00000000 + x = -67.251288397 + 71.59624415 x = -67.251288397 + 71.59624415 Combine like terms: -67.251288397 + 71.59624415 = 4.344955753 x = 4.344955753 Simplifying x = 4.344955753Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.847532547, 4.344955753}
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