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Simplifying 4x2 + 24x + -84 = 0 Reorder the terms: -84 + 24x + 4x2 = 0 Solving -84 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 6x + x2)' equal to zero and attempt to solve: Simplifying -21 + 6x + x2 = 0 Solving -21 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 6x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 6x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 6x + x2 = 0 + 21 6x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 6x + x2 = 21 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 21 + 9 Reorder the terms: 9 + 6x + x2 = 21 + 9 Combine like terms: 21 + 9 = 30 9 + 6x + x2 = 30 Factor a perfect square on the left side: (x + 3)(x + 3) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 3) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 3 = 5.477225575 Simplifying x + 3 = 5.477225575 Reorder the terms: 3 + x = 5.477225575 Solving 3 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.477225575 + -3 x = 5.477225575 + -3 Combine like terms: 5.477225575 + -3 = 2.477225575 x = 2.477225575 Simplifying x = 2.477225575Subproblem 2
x + 3 = -5.477225575 Simplifying x + 3 = -5.477225575 Reorder the terms: 3 + x = -5.477225575 Solving 3 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.477225575 + -3 x = -5.477225575 + -3 Combine like terms: -5.477225575 + -3 = -8.477225575 x = -8.477225575 Simplifying x = -8.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.477225575, -8.477225575}Solution
x = {2.477225575, -8.477225575}
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