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Simplifying x(2x + -3) + -3(5 + -83x) = 0 Reorder the terms: x(-3 + 2x) + -3(5 + -83x) = 0 (-3 * x + 2x * x) + -3(5 + -83x) = 0 (-3x + 2x2) + -3(5 + -83x) = 0 -3x + 2x2 + (5 * -3 + -83x * -3) = 0 -3x + 2x2 + (-15 + 249x) = 0 Reorder the terms: -15 + -3x + 249x + 2x2 = 0 Combine like terms: -3x + 249x = 246x -15 + 246x + 2x2 = 0 Solving -15 + 246x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 123x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 123x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 123x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 123x + x2 = 0 + 7.5 123x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 123x + x2 = 7.5 The x term is 123x. Take half its coefficient (61.5). Square it (3782.25) and add it to both sides. Add '3782.25' to each side of the equation. 123x + 3782.25 + x2 = 7.5 + 3782.25 Reorder the terms: 3782.25 + 123x + x2 = 7.5 + 3782.25 Combine like terms: 7.5 + 3782.25 = 3789.75 3782.25 + 123x + x2 = 3789.75 Factor a perfect square on the left side: (x + 61.5)(x + 61.5) = 3789.75 Calculate the square root of the right side: 61.560945412 Break this problem into two subproblems by setting (x + 61.5) equal to 61.560945412 and -61.560945412.Subproblem 1
x + 61.5 = 61.560945412 Simplifying x + 61.5 = 61.560945412 Reorder the terms: 61.5 + x = 61.560945412 Solving 61.5 + x = 61.560945412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.5' to each side of the equation. 61.5 + -61.5 + x = 61.560945412 + -61.5 Combine like terms: 61.5 + -61.5 = 0.0 0.0 + x = 61.560945412 + -61.5 x = 61.560945412 + -61.5 Combine like terms: 61.560945412 + -61.5 = 0.060945412 x = 0.060945412 Simplifying x = 0.060945412Subproblem 2
x + 61.5 = -61.560945412 Simplifying x + 61.5 = -61.560945412 Reorder the terms: 61.5 + x = -61.560945412 Solving 61.5 + x = -61.560945412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.5' to each side of the equation. 61.5 + -61.5 + x = -61.560945412 + -61.5 Combine like terms: 61.5 + -61.5 = 0.0 0.0 + x = -61.560945412 + -61.5 x = -61.560945412 + -61.5 Combine like terms: -61.560945412 + -61.5 = -123.060945412 x = -123.060945412 Simplifying x = -123.060945412Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.060945412, -123.060945412}
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