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Simplifying -6x + 2 + -4x(x + 1) = 6x + 3 Reorder the terms: -6x + 2 + -4x(1 + x) = 6x + 3 -6x + 2 + (1 * -4x + x * -4x) = 6x + 3 -6x + 2 + (-4x + -4x2) = 6x + 3 Reorder the terms: 2 + -6x + -4x + -4x2 = 6x + 3 Combine like terms: -6x + -4x = -10x 2 + -10x + -4x2 = 6x + 3 Reorder the terms: 2 + -10x + -4x2 = 3 + 6x Solving 2 + -10x + -4x2 = 3 + 6x Solving for variable 'x'. Reorder the terms: 2 + -3 + -10x + -6x + -4x2 = 3 + 6x + -3 + -6x Combine like terms: 2 + -3 = -1 -1 + -10x + -6x + -4x2 = 3 + 6x + -3 + -6x Combine like terms: -10x + -6x = -16x -1 + -16x + -4x2 = 3 + 6x + -3 + -6x Reorder the terms: -1 + -16x + -4x2 = 3 + -3 + 6x + -6x Combine like terms: 3 + -3 = 0 -1 + -16x + -4x2 = 0 + 6x + -6x -1 + -16x + -4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 16x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 16x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 16x + 4x2 = 0 Solving 1 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 4x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 4x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 4x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 4x + x2 = 0 + -0.25 4x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 4x + x2 = -0.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.25 + 4 Reorder the terms: 4 + 4x + x2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + 4x + x2 = 3.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 2) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 2 = 1.936491673 Simplifying x + 2 = 1.936491673 Reorder the terms: 2 + x = 1.936491673 Solving 2 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.936491673 + -2 x = 1.936491673 + -2 Combine like terms: 1.936491673 + -2 = -0.063508327 x = -0.063508327 Simplifying x = -0.063508327Subproblem 2
x + 2 = -1.936491673 Simplifying x + 2 = -1.936491673 Reorder the terms: 2 + x = -1.936491673 Solving 2 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.936491673 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.936491673 + -2 x = -1.936491673 + -2 Combine like terms: -1.936491673 + -2 = -3.936491673 x = -3.936491673 Simplifying x = -3.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.063508327, -3.936491673}Solution
x = {-0.063508327, -3.936491673}
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