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Simplifying 4x2 + -195x + 1755 = 0 Reorder the terms: 1755 + -195x + 4x2 = 0 Solving 1755 + -195x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 438.75 + -48.75x + x2 = 0 Move the constant term to the right: Add '-438.75' to each side of the equation. 438.75 + -48.75x + -438.75 + x2 = 0 + -438.75 Reorder the terms: 438.75 + -438.75 + -48.75x + x2 = 0 + -438.75 Combine like terms: 438.75 + -438.75 = 0.00 0.00 + -48.75x + x2 = 0 + -438.75 -48.75x + x2 = 0 + -438.75 Combine like terms: 0 + -438.75 = -438.75 -48.75x + x2 = -438.75 The x term is -48.75x. Take half its coefficient (-24.375). Square it (594.140625) and add it to both sides. Add '594.140625' to each side of the equation. -48.75x + 594.140625 + x2 = -438.75 + 594.140625 Reorder the terms: 594.140625 + -48.75x + x2 = -438.75 + 594.140625 Combine like terms: -438.75 + 594.140625 = 155.390625 594.140625 + -48.75x + x2 = 155.390625 Factor a perfect square on the left side: (x + -24.375)(x + -24.375) = 155.390625 Calculate the square root of the right side: 12.465577604 Break this problem into two subproblems by setting (x + -24.375) equal to 12.465577604 and -12.465577604.Subproblem 1
x + -24.375 = 12.465577604 Simplifying x + -24.375 = 12.465577604 Reorder the terms: -24.375 + x = 12.465577604 Solving -24.375 + x = 12.465577604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.375' to each side of the equation. -24.375 + 24.375 + x = 12.465577604 + 24.375 Combine like terms: -24.375 + 24.375 = 0.000 0.000 + x = 12.465577604 + 24.375 x = 12.465577604 + 24.375 Combine like terms: 12.465577604 + 24.375 = 36.840577604 x = 36.840577604 Simplifying x = 36.840577604Subproblem 2
x + -24.375 = -12.465577604 Simplifying x + -24.375 = -12.465577604 Reorder the terms: -24.375 + x = -12.465577604 Solving -24.375 + x = -12.465577604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.375' to each side of the equation. -24.375 + 24.375 + x = -12.465577604 + 24.375 Combine like terms: -24.375 + 24.375 = 0.000 0.000 + x = -12.465577604 + 24.375 x = -12.465577604 + 24.375 Combine like terms: -12.465577604 + 24.375 = 11.909422396 x = 11.909422396 Simplifying x = 11.909422396Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.840577604, 11.909422396}
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