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Simplifying 24x2 + -1156x + -11520 = 0 Reorder the terms: -11520 + -1156x + 24x2 = 0 Solving -11520 + -1156x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2880 + -289x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2880 + -289x + 6x2)' equal to zero and attempt to solve: Simplifying -2880 + -289x + 6x2 = 0 Solving -2880 + -289x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -480 + -48.16666667x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + -48.16666667x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + -48.16666667x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + -48.16666667x + x2 = 0 + 480 -48.16666667x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 -48.16666667x + x2 = 480 The x term is -48.16666667x. Take half its coefficient (-24.08333334). Square it (580.0069448) and add it to both sides. Add '580.0069448' to each side of the equation. -48.16666667x + 580.0069448 + x2 = 480 + 580.0069448 Reorder the terms: 580.0069448 + -48.16666667x + x2 = 480 + 580.0069448 Combine like terms: 480 + 580.0069448 = 1060.0069448 580.0069448 + -48.16666667x + x2 = 1060.0069448 Factor a perfect square on the left side: (x + -24.08333334)(x + -24.08333334) = 1060.0069448 Calculate the square root of the right side: 32.557747846 Break this problem into two subproblems by setting (x + -24.08333334) equal to 32.557747846 and -32.557747846.Subproblem 1
x + -24.08333334 = 32.557747846 Simplifying x + -24.08333334 = 32.557747846 Reorder the terms: -24.08333334 + x = 32.557747846 Solving -24.08333334 + x = 32.557747846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.08333334' to each side of the equation. -24.08333334 + 24.08333334 + x = 32.557747846 + 24.08333334 Combine like terms: -24.08333334 + 24.08333334 = 0.00000000 0.00000000 + x = 32.557747846 + 24.08333334 x = 32.557747846 + 24.08333334 Combine like terms: 32.557747846 + 24.08333334 = 56.641081186 x = 56.641081186 Simplifying x = 56.641081186Subproblem 2
x + -24.08333334 = -32.557747846 Simplifying x + -24.08333334 = -32.557747846 Reorder the terms: -24.08333334 + x = -32.557747846 Solving -24.08333334 + x = -32.557747846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.08333334' to each side of the equation. -24.08333334 + 24.08333334 + x = -32.557747846 + 24.08333334 Combine like terms: -24.08333334 + 24.08333334 = 0.00000000 0.00000000 + x = -32.557747846 + 24.08333334 x = -32.557747846 + 24.08333334 Combine like terms: -32.557747846 + 24.08333334 = -8.474414506 x = -8.474414506 Simplifying x = -8.474414506Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.641081186, -8.474414506}Solution
x = {56.641081186, -8.474414506}
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