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Simplifying 4(x + 4) * x = 6 Reorder the terms: 4(4 + x) * x = 6 Reorder the terms for easier multiplication: 4x(4 + x) = 6 (4 * 4x + x * 4x) = 6 (16x + 4x2) = 6 Solving 16x + 4x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 16x + 4x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 8x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 8x + 2x2 = 0 Solving -3 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 4x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4x + x2 = 0 + 1.5 4x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4x + x2 = 1.5 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 = 1.5 + 4 Reorder the terms: 4 + 4x + x2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + 4x + x2 = 5.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + 2) equal to 2.34520788 and -2.34520788.Subproblem 1
x + 2 = 2.34520788 Simplifying x + 2 = 2.34520788 Reorder the terms: 2 + x = 2.34520788 Solving 2 + x = 2.34520788 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 = 2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.34520788 + -2 x = 2.34520788 + -2 Combine like terms: 2.34520788 + -2 = 0.34520788 x = 0.34520788 Simplifying x = 0.34520788Subproblem 2
x + 2 = -2.34520788 Simplifying x + 2 = -2.34520788 Reorder the terms: 2 + x = -2.34520788 Solving 2 + x = -2.34520788 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 = -2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.34520788 + -2 x = -2.34520788 + -2 Combine like terms: -2.34520788 + -2 = -4.34520788 x = -4.34520788 Simplifying x = -4.34520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34520788, -4.34520788}Solution
x = {0.34520788, -4.34520788}
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