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Simplifying 0 = 4(x2 + 6x + -2880) Reorder the terms: 0 = 4(-2880 + 6x + x2) 0 = (-2880 * 4 + 6x * 4 + x2 * 4) 0 = (-11520 + 24x + 4x2) Solving 0 = -11520 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 11520 = 11520 11520 + -24x + -4x2 = -11520 + 24x + 4x2 + 11520 + -24x + -4x2 Reorder the terms: 11520 + -24x + -4x2 = -11520 + 11520 + 24x + -24x + 4x2 + -4x2 Combine like terms: -11520 + 11520 = 0 11520 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 11520 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 11520 + -24x + -4x2 = 0 + 4x2 + -4x2 11520 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 11520 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2880 + -6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2880 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 2880 + -6x + -1x2 = 0 Solving 2880 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2880 + 6x + x2 = 0 Move the constant term to the right: Add '2880' to each side of the equation. -2880 + 6x + 2880 + x2 = 0 + 2880 Reorder the terms: -2880 + 2880 + 6x + x2 = 0 + 2880 Combine like terms: -2880 + 2880 = 0 0 + 6x + x2 = 0 + 2880 6x + x2 = 0 + 2880 Combine like terms: 0 + 2880 = 2880 6x + x2 = 2880 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 = 2880 + 9 Reorder the terms: 9 + 6x + x2 = 2880 + 9 Combine like terms: 2880 + 9 = 2889 9 + 6x + x2 = 2889 Factor a perfect square on the left side: (x + 3)(x + 3) = 2889 Calculate the square root of the right side: 53.749418602 Break this problem into two subproblems by setting (x + 3) equal to 53.749418602 and -53.749418602.Subproblem 1
x + 3 = 53.749418602 Simplifying x + 3 = 53.749418602 Reorder the terms: 3 + x = 53.749418602 Solving 3 + x = 53.749418602 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 = 53.749418602 + -3 Combine like terms: 3 + -3 = 0 0 + x = 53.749418602 + -3 x = 53.749418602 + -3 Combine like terms: 53.749418602 + -3 = 50.749418602 x = 50.749418602 Simplifying x = 50.749418602Subproblem 2
x + 3 = -53.749418602 Simplifying x + 3 = -53.749418602 Reorder the terms: 3 + x = -53.749418602 Solving 3 + x = -53.749418602 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 = -53.749418602 + -3 Combine like terms: 3 + -3 = 0 0 + x = -53.749418602 + -3 x = -53.749418602 + -3 Combine like terms: -53.749418602 + -3 = -56.749418602 x = -56.749418602 Simplifying x = -56.749418602Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.749418602, -56.749418602}Solution
x = {50.749418602, -56.749418602}
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