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Simplifying 18.75x + -1.25x2 + -63 = 0 Reorder the terms: -63 + 18.75x + -1.25x2 = 0 Solving -63 + 18.75x + -1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. 50.4 + -15x + x2 = 0 Move the constant term to the right: Add '-50.4' to each side of the equation. 50.4 + -15x + -50.4 + x2 = 0 + -50.4 Reorder the terms: 50.4 + -50.4 + -15x + x2 = 0 + -50.4 Combine like terms: 50.4 + -50.4 = 0.0 0.0 + -15x + x2 = 0 + -50.4 -15x + x2 = 0 + -50.4 Combine like terms: 0 + -50.4 = -50.4 -15x + x2 = -50.4 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -50.4 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -50.4 + 56.25 Combine like terms: -50.4 + 56.25 = 5.85 56.25 + -15x + x2 = 5.85 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 5.85 Calculate the square root of the right side: 2.418677324 Break this problem into two subproblems by setting (x + -7.5) equal to 2.418677324 and -2.418677324.Subproblem 1
x + -7.5 = 2.418677324 Simplifying x + -7.5 = 2.418677324 Reorder the terms: -7.5 + x = 2.418677324 Solving -7.5 + x = 2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 2.418677324 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 2.418677324 + 7.5 x = 2.418677324 + 7.5 Combine like terms: 2.418677324 + 7.5 = 9.918677324 x = 9.918677324 Simplifying x = 9.918677324Subproblem 2
x + -7.5 = -2.418677324 Simplifying x + -7.5 = -2.418677324 Reorder the terms: -7.5 + x = -2.418677324 Solving -7.5 + x = -2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -2.418677324 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -2.418677324 + 7.5 x = -2.418677324 + 7.5 Combine like terms: -2.418677324 + 7.5 = 5.081322676 x = 5.081322676 Simplifying x = 5.081322676Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.918677324, 5.081322676}
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