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Simplifying 18x2 + 10x + -288 = 0 Reorder the terms: -288 + 10x + 18x2 = 0 Solving -288 + 10x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-144 + 5x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-144 + 5x + 9x2)' equal to zero and attempt to solve: Simplifying -144 + 5x + 9x2 = 0 Solving -144 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -16 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.5555555556x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.5555555556x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.5555555556x + x2 = 0 + 16 0.5555555556x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.5555555556x + x2 = 16 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 16 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 16 + 0.07716049384 Combine like terms: 16 + 0.07716049384 = 16.07716049384 0.07716049384 + 0.5555555556x + x2 = 16.07716049384 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 16.07716049384 Calculate the square root of the right side: 4.009633461 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 4.009633461 and -4.009633461.Subproblem 1
x + 0.2777777778 = 4.009633461 Simplifying x + 0.2777777778 = 4.009633461 Reorder the terms: 0.2777777778 + x = 4.009633461 Solving 0.2777777778 + x = 4.009633461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 4.009633461 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 4.009633461 + -0.2777777778 x = 4.009633461 + -0.2777777778 Combine like terms: 4.009633461 + -0.2777777778 = 3.7318556832 x = 3.7318556832 Simplifying x = 3.7318556832Subproblem 2
x + 0.2777777778 = -4.009633461 Simplifying x + 0.2777777778 = -4.009633461 Reorder the terms: 0.2777777778 + x = -4.009633461 Solving 0.2777777778 + x = -4.009633461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -4.009633461 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -4.009633461 + -0.2777777778 x = -4.009633461 + -0.2777777778 Combine like terms: -4.009633461 + -0.2777777778 = -4.2874112388 x = -4.2874112388 Simplifying x = -4.2874112388Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7318556832, -4.2874112388}Solution
x = {3.7318556832, -4.2874112388}
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