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Simplifying 2x + 4x(x + 5) + -1(3x + 7) = 16 + -5(2x + 3) Reorder the terms: 2x + 4x(5 + x) + -1(3x + 7) = 16 + -5(2x + 3) 2x + (5 * 4x + x * 4x) + -1(3x + 7) = 16 + -5(2x + 3) 2x + (20x + 4x2) + -1(3x + 7) = 16 + -5(2x + 3) Reorder the terms: 2x + 20x + 4x2 + -1(7 + 3x) = 16 + -5(2x + 3) 2x + 20x + 4x2 + (7 * -1 + 3x * -1) = 16 + -5(2x + 3) 2x + 20x + 4x2 + (-7 + -3x) = 16 + -5(2x + 3) Reorder the terms: -7 + 2x + 20x + -3x + 4x2 = 16 + -5(2x + 3) Combine like terms: 2x + 20x = 22x -7 + 22x + -3x + 4x2 = 16 + -5(2x + 3) Combine like terms: 22x + -3x = 19x -7 + 19x + 4x2 = 16 + -5(2x + 3) Reorder the terms: -7 + 19x + 4x2 = 16 + -5(3 + 2x) -7 + 19x + 4x2 = 16 + (3 * -5 + 2x * -5) -7 + 19x + 4x2 = 16 + (-15 + -10x) Combine like terms: 16 + -15 = 1 -7 + 19x + 4x2 = 1 + -10x Solving -7 + 19x + 4x2 = 1 + -10x Solving for variable 'x'. Reorder the terms: -7 + -1 + 19x + 10x + 4x2 = 1 + -10x + -1 + 10x Combine like terms: -7 + -1 = -8 -8 + 19x + 10x + 4x2 = 1 + -10x + -1 + 10x Combine like terms: 19x + 10x = 29x -8 + 29x + 4x2 = 1 + -10x + -1 + 10x Reorder the terms: -8 + 29x + 4x2 = 1 + -1 + -10x + 10x Combine like terms: 1 + -1 = 0 -8 + 29x + 4x2 = 0 + -10x + 10x -8 + 29x + 4x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -8 + 29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 7.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 7.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 7.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7.25x + x2 = 0 + 2 7.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 7.25x + x2 = 2 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 2 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 2 + 13.140625 Combine like terms: 2 + 13.140625 = 15.140625 13.140625 + 7.25x + x2 = 15.140625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + 3.625) equal to 3.891095604 and -3.891095604.Subproblem 1
x + 3.625 = 3.891095604 Simplifying x + 3.625 = 3.891095604 Reorder the terms: 3.625 + x = 3.891095604 Solving 3.625 + x = 3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 3.891095604 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 3.891095604 + -3.625 x = 3.891095604 + -3.625 Combine like terms: 3.891095604 + -3.625 = 0.266095604 x = 0.266095604 Simplifying x = 0.266095604Subproblem 2
x + 3.625 = -3.891095604 Simplifying x + 3.625 = -3.891095604 Reorder the terms: 3.625 + x = -3.891095604 Solving 3.625 + x = -3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -3.891095604 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -3.891095604 + -3.625 x = -3.891095604 + -3.625 Combine like terms: -3.891095604 + -3.625 = -7.516095604 x = -7.516095604 Simplifying x = -7.516095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.266095604, -7.516095604}
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