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Simplifying (4x + -6)(2x + 1) = (-0.5) Reorder the terms: (-6 + 4x)(2x + 1) = (-0.5) Reorder the terms: (-6 + 4x)(1 + 2x) = (-0.5) Multiply (-6 + 4x) * (1 + 2x) (-6(1 + 2x) + 4x * (1 + 2x)) = (-0.5) ((1 * -6 + 2x * -6) + 4x * (1 + 2x)) = (-0.5) ((-6 + -12x) + 4x * (1 + 2x)) = (-0.5) (-6 + -12x + (1 * 4x + 2x * 4x)) = (-0.5) (-6 + -12x + (4x + 8x2)) = (-0.5) Combine like terms: -12x + 4x = -8x (-6 + -8x + 8x2) = (-0.5) -6 + -8x + 8x2 = -0.5 Solving -6 + -8x + 8x2 = -0.5 Solving for variable 'x'. Reorder the terms: -6 + 0.5 + -8x + 8x2 = -0.5 + 0.5 Combine like terms: -6 + 0.5 = -5.5 -5.5 + -8x + 8x2 = -0.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 -5.5 + -8x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.6875 + -1x + x2 = 0.0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -1x + 0.6875 + x2 = 0.0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -1x + x2 = 0.0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -1x + x2 = 0.0 + 0.6875 -1x + x2 = 0.0 + 0.6875 Combine like terms: 0.0 + 0.6875 = 0.6875 -1x + x2 = 0.6875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.6875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.6875 + 0.25 Combine like terms: 0.6875 + 0.25 = 0.9375 0.25 + -1x + x2 = 0.9375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (x + -0.5) equal to 0.968245837 and -0.968245837.Subproblem 1
x + -0.5 = 0.968245837 Simplifying x + -0.5 = 0.968245837 Reorder the terms: -0.5 + x = 0.968245837 Solving -0.5 + x = 0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.968245837 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.968245837 + 0.5 x = 0.968245837 + 0.5 Combine like terms: 0.968245837 + 0.5 = 1.468245837 x = 1.468245837 Simplifying x = 1.468245837Subproblem 2
x + -0.5 = -0.968245837 Simplifying x + -0.5 = -0.968245837 Reorder the terms: -0.5 + x = -0.968245837 Solving -0.5 + x = -0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.968245837 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.968245837 + 0.5 x = -0.968245837 + 0.5 Combine like terms: -0.968245837 + 0.5 = -0.468245837 x = -0.468245837 Simplifying x = -0.468245837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.468245837, -0.468245837}
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