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Simplifying 5x + x(3 + 2x) = 18 + -1(x + -1) 5x + (3 * x + 2x * x) = 18 + -1(x + -1) 5x + (3x + 2x2) = 18 + -1(x + -1) Combine like terms: 5x + 3x = 8x 8x + 2x2 = 18 + -1(x + -1) Reorder the terms: 8x + 2x2 = 18 + -1(-1 + x) 8x + 2x2 = 18 + (-1 * -1 + x * -1) 8x + 2x2 = 18 + (1 + -1x) Combine like terms: 18 + 1 = 19 8x + 2x2 = 19 + -1x Solving 8x + 2x2 = 19 + -1x Solving for variable 'x'. Reorder the terms: -19 + 8x + x + 2x2 = 19 + -1x + -19 + x Combine like terms: 8x + x = 9x -19 + 9x + 2x2 = 19 + -1x + -19 + x Reorder the terms: -19 + 9x + 2x2 = 19 + -19 + -1x + x Combine like terms: 19 + -19 = 0 -19 + 9x + 2x2 = 0 + -1x + x -19 + 9x + 2x2 = -1x + x Combine like terms: -1x + x = 0 -19 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 4.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 4.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 4.5x + x2 = 0 + 9.5 4.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 4.5x + x2 = 9.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 9.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 9.5 + 5.0625 Combine like terms: 9.5 + 5.0625 = 14.5625 5.0625 + 4.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 2.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 2.25 = 3.816084381 Simplifying x + 2.25 = 3.816084381 Reorder the terms: 2.25 + x = 3.816084381 Solving 2.25 + x = 3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.816084381 + -2.25 x = 3.816084381 + -2.25 Combine like terms: 3.816084381 + -2.25 = 1.566084381 x = 1.566084381 Simplifying x = 1.566084381Subproblem 2
x + 2.25 = -3.816084381 Simplifying x + 2.25 = -3.816084381 Reorder the terms: 2.25 + x = -3.816084381 Solving 2.25 + x = -3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.816084381 + -2.25 x = -3.816084381 + -2.25 Combine like terms: -3.816084381 + -2.25 = -6.066084381 x = -6.066084381 Simplifying x = -6.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.566084381, -6.066084381}
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