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Simplifying 16x2 + 75x = 28 Reorder the terms: 75x + 16x2 = 28 Solving 75x + 16x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 75x + 16x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 75x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.75 + 4.6875x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 4.6875x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 4.6875x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 4.6875x + x2 = 0 + 1.75 4.6875x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 4.6875x + x2 = 1.75 The x term is 4.6875x. Take half its coefficient (2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. 4.6875x + 5.493164063 + x2 = 1.75 + 5.493164063 Reorder the terms: 5.493164063 + 4.6875x + x2 = 1.75 + 5.493164063 Combine like terms: 1.75 + 5.493164063 = 7.243164063 5.493164063 + 4.6875x + x2 = 7.243164063 Factor a perfect square on the left side: (x + 2.34375)(x + 2.34375) = 7.243164063 Calculate the square root of the right side: 2.691312703 Break this problem into two subproblems by setting (x + 2.34375) equal to 2.691312703 and -2.691312703.Subproblem 1
x + 2.34375 = 2.691312703 Simplifying x + 2.34375 = 2.691312703 Reorder the terms: 2.34375 + x = 2.691312703 Solving 2.34375 + x = 2.691312703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + x = 2.691312703 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + x = 2.691312703 + -2.34375 x = 2.691312703 + -2.34375 Combine like terms: 2.691312703 + -2.34375 = 0.347562703 x = 0.347562703 Simplifying x = 0.347562703Subproblem 2
x + 2.34375 = -2.691312703 Simplifying x + 2.34375 = -2.691312703 Reorder the terms: 2.34375 + x = -2.691312703 Solving 2.34375 + x = -2.691312703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + x = -2.691312703 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + x = -2.691312703 + -2.34375 x = -2.691312703 + -2.34375 Combine like terms: -2.691312703 + -2.34375 = -5.035062703 x = -5.035062703 Simplifying x = -5.035062703Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.347562703, -5.035062703}
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