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Simplifying 0 = 8x2 + 24x + -5560 Reorder the terms: 0 = -5560 + 24x + 8x2 Solving 0 = -5560 + 24x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 5560 = 5560 5560 + -24x + -8x2 = -5560 + 24x + 8x2 + 5560 + -24x + -8x2 Reorder the terms: 5560 + -24x + -8x2 = -5560 + 5560 + 24x + -24x + 8x2 + -8x2 Combine like terms: -5560 + 5560 = 0 5560 + -24x + -8x2 = 0 + 24x + -24x + 8x2 + -8x2 5560 + -24x + -8x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 5560 + -24x + -8x2 = 0 + 8x2 + -8x2 5560 + -24x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 5560 + -24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(695 + -3x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(695 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 695 + -3x + -1x2 = 0 Solving 695 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -695 + 3x + x2 = 0 Move the constant term to the right: Add '695' to each side of the equation. -695 + 3x + 695 + x2 = 0 + 695 Reorder the terms: -695 + 695 + 3x + x2 = 0 + 695 Combine like terms: -695 + 695 = 0 0 + 3x + x2 = 0 + 695 3x + x2 = 0 + 695 Combine like terms: 0 + 695 = 695 3x + x2 = 695 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 = 695 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 695 + 2.25 Combine like terms: 695 + 2.25 = 697.25 2.25 + 3x + x2 = 697.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 697.25 Calculate the square root of the right side: 26.405491853 Break this problem into two subproblems by setting (x + 1.5) equal to 26.405491853 and -26.405491853.Subproblem 1
x + 1.5 = 26.405491853 Simplifying x + 1.5 = 26.405491853 Reorder the terms: 1.5 + x = 26.405491853 Solving 1.5 + x = 26.405491853 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 = 26.405491853 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 26.405491853 + -1.5 x = 26.405491853 + -1.5 Combine like terms: 26.405491853 + -1.5 = 24.905491853 x = 24.905491853 Simplifying x = 24.905491853Subproblem 2
x + 1.5 = -26.405491853 Simplifying x + 1.5 = -26.405491853 Reorder the terms: 1.5 + x = -26.405491853 Solving 1.5 + x = -26.405491853 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 = -26.405491853 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -26.405491853 + -1.5 x = -26.405491853 + -1.5 Combine like terms: -26.405491853 + -1.5 = -27.905491853 x = -27.905491853 Simplifying x = -27.905491853Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.905491853, -27.905491853}Solution
x = {24.905491853, -27.905491853}
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