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Simplifying 576 + -16x2 = 4.9x2 + -4.9x Reorder the terms: 576 + -16x2 = -4.9x + 4.9x2 Solving 576 + -16x2 = -4.9x + 4.9x2 Solving for variable 'x'. Reorder the terms: 576 + 4.9x + -16x2 + -4.9x2 = -4.9x + 4.9x2 + 4.9x + -4.9x2 Combine like terms: -16x2 + -4.9x2 = -20.9x2 576 + 4.9x + -20.9x2 = -4.9x + 4.9x2 + 4.9x + -4.9x2 Reorder the terms: 576 + 4.9x + -20.9x2 = -4.9x + 4.9x + 4.9x2 + -4.9x2 Combine like terms: -4.9x + 4.9x = 0.0 576 + 4.9x + -20.9x2 = 0.0 + 4.9x2 + -4.9x2 576 + 4.9x + -20.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 576 + 4.9x + -20.9x2 = 0.0 Begin completing the square. Divide all terms by -20.9 the coefficient of the squared term: Divide each side by '-20.9'. -27.55980861 + -0.2344497608x + x2 = 0 Move the constant term to the right: Add '27.55980861' to each side of the equation. -27.55980861 + -0.2344497608x + 27.55980861 + x2 = 0 + 27.55980861 Reorder the terms: -27.55980861 + 27.55980861 + -0.2344497608x + x2 = 0 + 27.55980861 Combine like terms: -27.55980861 + 27.55980861 = 0.00000000 0.00000000 + -0.2344497608x + x2 = 0 + 27.55980861 -0.2344497608x + x2 = 0 + 27.55980861 Combine like terms: 0 + 27.55980861 = 27.55980861 -0.2344497608x + x2 = 27.55980861 The x term is -0.2344497608x. Take half its coefficient (-0.1172248804). Square it (0.01374167258) and add it to both sides. Add '0.01374167258' to each side of the equation. -0.2344497608x + 0.01374167258 + x2 = 27.55980861 + 0.01374167258 Reorder the terms: 0.01374167258 + -0.2344497608x + x2 = 27.55980861 + 0.01374167258 Combine like terms: 27.55980861 + 0.01374167258 = 27.57355028258 0.01374167258 + -0.2344497608x + x2 = 27.57355028258 Factor a perfect square on the left side: (x + -0.1172248804)(x + -0.1172248804) = 27.57355028258 Calculate the square root of the right side: 5.251052302 Break this problem into two subproblems by setting (x + -0.1172248804) equal to 5.251052302 and -5.251052302.Subproblem 1
x + -0.1172248804 = 5.251052302 Simplifying x + -0.1172248804 = 5.251052302 Reorder the terms: -0.1172248804 + x = 5.251052302 Solving -0.1172248804 + x = 5.251052302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1172248804' to each side of the equation. -0.1172248804 + 0.1172248804 + x = 5.251052302 + 0.1172248804 Combine like terms: -0.1172248804 + 0.1172248804 = 0.0000000000 0.0000000000 + x = 5.251052302 + 0.1172248804 x = 5.251052302 + 0.1172248804 Combine like terms: 5.251052302 + 0.1172248804 = 5.3682771824 x = 5.3682771824 Simplifying x = 5.3682771824Subproblem 2
x + -0.1172248804 = -5.251052302 Simplifying x + -0.1172248804 = -5.251052302 Reorder the terms: -0.1172248804 + x = -5.251052302 Solving -0.1172248804 + x = -5.251052302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1172248804' to each side of the equation. -0.1172248804 + 0.1172248804 + x = -5.251052302 + 0.1172248804 Combine like terms: -0.1172248804 + 0.1172248804 = 0.0000000000 0.0000000000 + x = -5.251052302 + 0.1172248804 x = -5.251052302 + 0.1172248804 Combine like terms: -5.251052302 + 0.1172248804 = -5.1338274216 x = -5.1338274216 Simplifying x = -5.1338274216Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3682771824, -5.1338274216}
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