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Simplifying -6(4x + 3) * 4x + 8 = 0 Reorder the terms: -6(3 + 4x) * 4x + 8 = 0 Reorder the terms for easier multiplication: -6 * 4x(3 + 4x) + 8 = 0 Multiply -6 * 4 -24x(3 + 4x) + 8 = 0 (3 * -24x + 4x * -24x) + 8 = 0 (-72x + -96x2) + 8 = 0 Reorder the terms: 8 + -72x + -96x2 = 0 Solving 8 + -72x + -96x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(1 + -9x + -12x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -9x + -12x2)' equal to zero and attempt to solve: Simplifying 1 + -9x + -12x2 = 0 Solving 1 + -9x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.75x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.75x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.75x + x2 = 0 + 0.08333333333 0.75x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.75x + x2 = 0.08333333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.08333333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.08333333333 + 0.140625 Combine like terms: 0.08333333333 + 0.140625 = 0.22395833333 0.140625 + 0.75x + x2 = 0.22395833333 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.22395833333 Calculate the square root of the right side: 0.473242362 Break this problem into two subproblems by setting (x + 0.375) equal to 0.473242362 and -0.473242362.Subproblem 1
x + 0.375 = 0.473242362 Simplifying x + 0.375 = 0.473242362 Reorder the terms: 0.375 + x = 0.473242362 Solving 0.375 + x = 0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.473242362 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.473242362 + -0.375 x = 0.473242362 + -0.375 Combine like terms: 0.473242362 + -0.375 = 0.098242362 x = 0.098242362 Simplifying x = 0.098242362Subproblem 2
x + 0.375 = -0.473242362 Simplifying x + 0.375 = -0.473242362 Reorder the terms: 0.375 + x = -0.473242362 Solving 0.375 + x = -0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.473242362 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.473242362 + -0.375 x = -0.473242362 + -0.375 Combine like terms: -0.473242362 + -0.375 = -0.848242362 x = -0.848242362 Simplifying x = -0.848242362Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.098242362, -0.848242362}Solution
x = {0.098242362, -0.848242362}
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