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Simplifying 4x2 + 24x + -224 = 0 Reorder the terms: -224 + 24x + 4x2 = 0 Solving -224 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-56 + 6x + x2)' equal to zero and attempt to solve: Simplifying -56 + 6x + x2 = 0 Solving -56 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 6x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 6x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 6x + x2 = 0 + 56 6x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 6x + x2 = 56 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 = 56 + 9 Reorder the terms: 9 + 6x + x2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + 6x + x2 = 65 Factor a perfect square on the left side: (x + 3)(x + 3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 3) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 3 = 8.062257748 Simplifying x + 3 = 8.062257748 Reorder the terms: 3 + x = 8.062257748 Solving 3 + x = 8.062257748 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 = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.062257748 + -3 x = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 x = 5.062257748 Simplifying x = 5.062257748Subproblem 2
x + 3 = -8.062257748 Simplifying x + 3 = -8.062257748 Reorder the terms: 3 + x = -8.062257748 Solving 3 + x = -8.062257748 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 = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.062257748 + -3 x = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 x = -11.062257748 Simplifying x = -11.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.062257748, -11.062257748}Solution
x = {5.062257748, -11.062257748}
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