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Simplifying 9x + 3 + -90x2 + 144 = 0 Reorder the terms: 3 + 144 + 9x + -90x2 = 0 Combine like terms: 3 + 144 = 147 147 + 9x + -90x2 = 0 Solving 147 + 9x + -90x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(49 + 3x + -30x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(49 + 3x + -30x2)' equal to zero and attempt to solve: Simplifying 49 + 3x + -30x2 = 0 Solving 49 + 3x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. -1.633333333 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '1.633333333' to each side of the equation. -1.633333333 + -0.1x + 1.633333333 + x2 = 0.0 + 1.633333333 Reorder the terms: -1.633333333 + 1.633333333 + -0.1x + x2 = 0.0 + 1.633333333 Combine like terms: -1.633333333 + 1.633333333 = 0.000000000 0.000000000 + -0.1x + x2 = 0.0 + 1.633333333 -0.1x + x2 = 0.0 + 1.633333333 Combine like terms: 0.0 + 1.633333333 = 1.633333333 -0.1x + x2 = 1.633333333 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 1.633333333 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 1.633333333 + 0.0025 Combine like terms: 1.633333333 + 0.0025 = 1.635833333 0.0025 + -0.1x + x2 = 1.635833333 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 1.635833333 Calculate the square root of the right side: 1.278997003 Break this problem into two subproblems by setting (x + -0.05) equal to 1.278997003 and -1.278997003.Subproblem 1
x + -0.05 = 1.278997003 Simplifying x + -0.05 = 1.278997003 Reorder the terms: -0.05 + x = 1.278997003 Solving -0.05 + x = 1.278997003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.278997003 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.278997003 + 0.05 x = 1.278997003 + 0.05 Combine like terms: 1.278997003 + 0.05 = 1.328997003 x = 1.328997003 Simplifying x = 1.328997003Subproblem 2
x + -0.05 = -1.278997003 Simplifying x + -0.05 = -1.278997003 Reorder the terms: -0.05 + x = -1.278997003 Solving -0.05 + x = -1.278997003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.278997003 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.278997003 + 0.05 x = -1.278997003 + 0.05 Combine like terms: -1.278997003 + 0.05 = -1.228997003 x = -1.228997003 Simplifying x = -1.228997003Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.328997003, -1.228997003}Solution
x = {1.328997003, -1.228997003}
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