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Simplifying x2 + -1(77.4) * x + 14.1 = 0 Multiply -1 * 77.4 x2 + -77.4x + 14.1 = 0 Reorder the terms: 14.1 + -77.4x + x2 = 0 Solving 14.1 + -77.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14.1' to each side of the equation. 14.1 + -77.4x + -14.1 + x2 = 0 + -14.1 Reorder the terms: 14.1 + -14.1 + -77.4x + x2 = 0 + -14.1 Combine like terms: 14.1 + -14.1 = 0.0 0.0 + -77.4x + x2 = 0 + -14.1 -77.4x + x2 = 0 + -14.1 Combine like terms: 0 + -14.1 = -14.1 -77.4x + x2 = -14.1 The x term is -77.4x. Take half its coefficient (-38.7). Square it (1497.69) and add it to both sides. Add '1497.69' to each side of the equation. -77.4x + 1497.69 + x2 = -14.1 + 1497.69 Reorder the terms: 1497.69 + -77.4x + x2 = -14.1 + 1497.69 Combine like terms: -14.1 + 1497.69 = 1483.59 1497.69 + -77.4x + x2 = 1483.59 Factor a perfect square on the left side: (x + -38.7)(x + -38.7) = 1483.59 Calculate the square root of the right side: 38.517398666 Break this problem into two subproblems by setting (x + -38.7) equal to 38.517398666 and -38.517398666.Subproblem 1
x + -38.7 = 38.517398666 Simplifying x + -38.7 = 38.517398666 Reorder the terms: -38.7 + x = 38.517398666 Solving -38.7 + x = 38.517398666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.7' to each side of the equation. -38.7 + 38.7 + x = 38.517398666 + 38.7 Combine like terms: -38.7 + 38.7 = 0.0 0.0 + x = 38.517398666 + 38.7 x = 38.517398666 + 38.7 Combine like terms: 38.517398666 + 38.7 = 77.217398666 x = 77.217398666 Simplifying x = 77.217398666Subproblem 2
x + -38.7 = -38.517398666 Simplifying x + -38.7 = -38.517398666 Reorder the terms: -38.7 + x = -38.517398666 Solving -38.7 + x = -38.517398666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.7' to each side of the equation. -38.7 + 38.7 + x = -38.517398666 + 38.7 Combine like terms: -38.7 + 38.7 = 0.0 0.0 + x = -38.517398666 + 38.7 x = -38.517398666 + 38.7 Combine like terms: -38.517398666 + 38.7 = 0.182601334 x = 0.182601334 Simplifying x = 0.182601334Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.217398666, 0.182601334}
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