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Simplifying 6x + -1(2x + -1)(2x + 1) = 2 + -1(3 + 2x) * 2 Reorder the terms: 6x + -1(-1 + 2x)(2x + 1) = 2 + -1(3 + 2x) * 2 Reorder the terms: 6x + -1(-1 + 2x)(1 + 2x) = 2 + -1(3 + 2x) * 2 Multiply (-1 + 2x) * (1 + 2x) 6x + -1(-1(1 + 2x) + 2x * (1 + 2x)) = 2 + -1(3 + 2x) * 2 6x + -1((1 * -1 + 2x * -1) + 2x * (1 + 2x)) = 2 + -1(3 + 2x) * 2 6x + -1((-1 + -2x) + 2x * (1 + 2x)) = 2 + -1(3 + 2x) * 2 6x + -1(-1 + -2x + (1 * 2x + 2x * 2x)) = 2 + -1(3 + 2x) * 2 6x + -1(-1 + -2x + (2x + 4x2)) = 2 + -1(3 + 2x) * 2 Combine like terms: -2x + 2x = 0 6x + -1(-1 + 0 + 4x2) = 2 + -1(3 + 2x) * 2 6x + -1(-1 + 4x2) = 2 + -1(3 + 2x) * 2 6x + (-1 * -1 + 4x2 * -1) = 2 + -1(3 + 2x) * 2 6x + (1 + -4x2) = 2 + -1(3 + 2x) * 2 Reorder the terms: 1 + 6x + -4x2 = 2 + -1(3 + 2x) * 2 Reorder the terms for easier multiplication: 1 + 6x + -4x2 = 2 + -1 * 2(3 + 2x) Multiply -1 * 2 1 + 6x + -4x2 = 2 + -2(3 + 2x) 1 + 6x + -4x2 = 2 + (3 * -2 + 2x * -2) 1 + 6x + -4x2 = 2 + (-6 + -4x) Combine like terms: 2 + -6 = -4 1 + 6x + -4x2 = -4 + -4x Solving 1 + 6x + -4x2 = -4 + -4x Solving for variable 'x'. Reorder the terms: 1 + 4 + 6x + 4x + -4x2 = -4 + -4x + 4 + 4x Combine like terms: 1 + 4 = 5 5 + 6x + 4x + -4x2 = -4 + -4x + 4 + 4x Combine like terms: 6x + 4x = 10x 5 + 10x + -4x2 = -4 + -4x + 4 + 4x Reorder the terms: 5 + 10x + -4x2 = -4 + 4 + -4x + 4x Combine like terms: -4 + 4 = 0 5 + 10x + -4x2 = 0 + -4x + 4x 5 + 10x + -4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 5 + 10x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.5x + x2 = 0 + 1.25 -2.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.5x + x2 = 1.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.25 + 1.5625 Combine like terms: 1.25 + 1.5625 = 2.8125 1.5625 + -2.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -1.25) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -1.25 = 1.677050983 Simplifying x + -1.25 = 1.677050983 Reorder the terms: -1.25 + x = 1.677050983 Solving -1.25 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.677050983 + 1.25 x = 1.677050983 + 1.25 Combine like terms: 1.677050983 + 1.25 = 2.927050983 x = 2.927050983 Simplifying x = 2.927050983Subproblem 2
x + -1.25 = -1.677050983 Simplifying x + -1.25 = -1.677050983 Reorder the terms: -1.25 + x = -1.677050983 Solving -1.25 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.677050983 + 1.25 x = -1.677050983 + 1.25 Combine like terms: -1.677050983 + 1.25 = -0.427050983 x = -0.427050983 Simplifying x = -0.427050983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.927050983, -0.427050983}
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