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Simplifying 4x(4x) + 12x + -48 = 0 Remove parenthesis around (4x) 4x * 4x + 12x + -48 = 0 Reorder the terms for easier multiplication: 4 * 4x * x + 12x + -48 = 0 Multiply 4 * 4 16x * x + 12x + -48 = 0 Multiply x * x 16x2 + 12x + -48 = 0 Reorder the terms: -48 + 12x + 16x2 = 0 Solving -48 + 12x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + 3x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -12 + 3x + 4x2 = 0 Solving -12 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 0.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.75x + x2 = 0 + 3 0.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.75x + x2 = 3 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 = 3 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 3 + 0.140625 Combine like terms: 3 + 0.140625 = 3.140625 0.140625 + 0.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 0.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 0.375 = 1.77218086 Simplifying x + 0.375 = 1.77218086 Reorder the terms: 0.375 + x = 1.77218086 Solving 0.375 + x = 1.77218086 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 = 1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.77218086 + -0.375 x = 1.77218086 + -0.375 Combine like terms: 1.77218086 + -0.375 = 1.39718086 x = 1.39718086 Simplifying x = 1.39718086Subproblem 2
x + 0.375 = -1.77218086 Simplifying x + 0.375 = -1.77218086 Reorder the terms: 0.375 + x = -1.77218086 Solving 0.375 + x = -1.77218086 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 = -1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.77218086 + -0.375 x = -1.77218086 + -0.375 Combine like terms: -1.77218086 + -0.375 = -2.14718086 x = -2.14718086 Simplifying x = -2.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.39718086, -2.14718086}Solution
x = {1.39718086, -2.14718086}
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