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Simplifying 4x2 + 12x + -424 = 0 Reorder the terms: -424 + 12x + 4x2 = 0 Solving -424 + 12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-106 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-106 + 3x + x2)' equal to zero and attempt to solve: Simplifying -106 + 3x + x2 = 0 Solving -106 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + 3x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 3x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 3x + x2 = 0 + 106 3x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 3x + x2 = 106 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 106 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 106 + 2.25 Combine like terms: 106 + 2.25 = 108.25 2.25 + 3x + x2 = 108.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + 1.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + 1.5 = 10.404326023 Simplifying x + 1.5 = 10.404326023 Reorder the terms: 1.5 + x = 10.404326023 Solving 1.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.404326023 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.404326023 + -1.5 x = 10.404326023 + -1.5 Combine like terms: 10.404326023 + -1.5 = 8.904326023 x = 8.904326023 Simplifying x = 8.904326023Subproblem 2
x + 1.5 = -10.404326023 Simplifying x + 1.5 = -10.404326023 Reorder the terms: 1.5 + x = -10.404326023 Solving 1.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.404326023 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.404326023 + -1.5 x = -10.404326023 + -1.5 Combine like terms: -10.404326023 + -1.5 = -11.904326023 x = -11.904326023 Simplifying x = -11.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.904326023, -11.904326023}Solution
x = {8.904326023, -11.904326023}
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