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Simplifying 50x2 + -75x + 25 = 4x2 Reorder the terms: 25 + -75x + 50x2 = 4x2 Solving 25 + -75x + 50x2 = 4x2 Solving for variable 'x'. Combine like terms: 50x2 + -4x2 = 46x2 25 + -75x + 46x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 25 + -75x + 46x2 = 0 Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. 0.5434782609 + -1.630434783x + x2 = 0 Move the constant term to the right: Add '-0.5434782609' to each side of the equation. 0.5434782609 + -1.630434783x + -0.5434782609 + x2 = 0 + -0.5434782609 Reorder the terms: 0.5434782609 + -0.5434782609 + -1.630434783x + x2 = 0 + -0.5434782609 Combine like terms: 0.5434782609 + -0.5434782609 = 0.0000000000 0.0000000000 + -1.630434783x + x2 = 0 + -0.5434782609 -1.630434783x + x2 = 0 + -0.5434782609 Combine like terms: 0 + -0.5434782609 = -0.5434782609 -1.630434783x + x2 = -0.5434782609 The x term is -1.630434783x. Take half its coefficient (-0.8152173915). Square it (0.6645793954) and add it to both sides. Add '0.6645793954' to each side of the equation. -1.630434783x + 0.6645793954 + x2 = -0.5434782609 + 0.6645793954 Reorder the terms: 0.6645793954 + -1.630434783x + x2 = -0.5434782609 + 0.6645793954 Combine like terms: -0.5434782609 + 0.6645793954 = 0.1211011345 0.6645793954 + -1.630434783x + x2 = 0.1211011345 Factor a perfect square on the left side: (x + -0.8152173915)(x + -0.8152173915) = 0.1211011345 Calculate the square root of the right side: 0.347995883 Break this problem into two subproblems by setting (x + -0.8152173915) equal to 0.347995883 and -0.347995883.Subproblem 1
x + -0.8152173915 = 0.347995883 Simplifying x + -0.8152173915 = 0.347995883 Reorder the terms: -0.8152173915 + x = 0.347995883 Solving -0.8152173915 + x = 0.347995883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8152173915' to each side of the equation. -0.8152173915 + 0.8152173915 + x = 0.347995883 + 0.8152173915 Combine like terms: -0.8152173915 + 0.8152173915 = 0.0000000000 0.0000000000 + x = 0.347995883 + 0.8152173915 x = 0.347995883 + 0.8152173915 Combine like terms: 0.347995883 + 0.8152173915 = 1.1632132745 x = 1.1632132745 Simplifying x = 1.1632132745Subproblem 2
x + -0.8152173915 = -0.347995883 Simplifying x + -0.8152173915 = -0.347995883 Reorder the terms: -0.8152173915 + x = -0.347995883 Solving -0.8152173915 + x = -0.347995883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8152173915' to each side of the equation. -0.8152173915 + 0.8152173915 + x = -0.347995883 + 0.8152173915 Combine like terms: -0.8152173915 + 0.8152173915 = 0.0000000000 0.0000000000 + x = -0.347995883 + 0.8152173915 x = -0.347995883 + 0.8152173915 Combine like terms: -0.347995883 + 0.8152173915 = 0.4672215085 x = 0.4672215085 Simplifying x = 0.4672215085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1632132745, 0.4672215085}
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