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Simplifying 45x + 3x2 = 256 Solving 45x + 3x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 45x + 3x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -85.33333333 + 15x + x2 = 0 Move the constant term to the right: Add '85.33333333' to each side of the equation. -85.33333333 + 15x + 85.33333333 + x2 = 0 + 85.33333333 Reorder the terms: -85.33333333 + 85.33333333 + 15x + x2 = 0 + 85.33333333 Combine like terms: -85.33333333 + 85.33333333 = 0.00000000 0.00000000 + 15x + x2 = 0 + 85.33333333 15x + x2 = 0 + 85.33333333 Combine like terms: 0 + 85.33333333 = 85.33333333 15x + x2 = 85.33333333 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 = 85.33333333 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 85.33333333 + 56.25 Combine like terms: 85.33333333 + 56.25 = 141.58333333 56.25 + 15x + x2 = 141.58333333 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 141.58333333 Calculate the square root of the right side: 11.898879499 Break this problem into two subproblems by setting (x + 7.5) equal to 11.898879499 and -11.898879499.Subproblem 1
x + 7.5 = 11.898879499 Simplifying x + 7.5 = 11.898879499 Reorder the terms: 7.5 + x = 11.898879499 Solving 7.5 + x = 11.898879499 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 = 11.898879499 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.898879499 + -7.5 x = 11.898879499 + -7.5 Combine like terms: 11.898879499 + -7.5 = 4.398879499 x = 4.398879499 Simplifying x = 4.398879499Subproblem 2
x + 7.5 = -11.898879499 Simplifying x + 7.5 = -11.898879499 Reorder the terms: 7.5 + x = -11.898879499 Solving 7.5 + x = -11.898879499 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 = -11.898879499 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.898879499 + -7.5 x = -11.898879499 + -7.5 Combine like terms: -11.898879499 + -7.5 = -19.398879499 x = -19.398879499 Simplifying x = -19.398879499Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.398879499, -19.398879499}
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