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Simplifying 144x2 + -2x + -122 = 0 Reorder the terms: -122 + -2x + 144x2 = 0 Solving -122 + -2x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + -1x + 72x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + -1x + 72x2)' equal to zero and attempt to solve: Simplifying -61 + -1x + 72x2 = 0 Solving -61 + -1x + 72x2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.8472222222 + -0.01388888889x + x2 = 0 Move the constant term to the right: Add '0.8472222222' to each side of the equation. -0.8472222222 + -0.01388888889x + 0.8472222222 + x2 = 0 + 0.8472222222 Reorder the terms: -0.8472222222 + 0.8472222222 + -0.01388888889x + x2 = 0 + 0.8472222222 Combine like terms: -0.8472222222 + 0.8472222222 = 0.0000000000 0.0000000000 + -0.01388888889x + x2 = 0 + 0.8472222222 -0.01388888889x + x2 = 0 + 0.8472222222 Combine like terms: 0 + 0.8472222222 = 0.8472222222 -0.01388888889x + x2 = 0.8472222222 The x term is -0.01388888889x. Take half its coefficient (-0.006944444445). Square it (0.00004822530865) and add it to both sides. Add '0.00004822530865' to each side of the equation. -0.01388888889x + 0.00004822530865 + x2 = 0.8472222222 + 0.00004822530865 Reorder the terms: 0.00004822530865 + -0.01388888889x + x2 = 0.8472222222 + 0.00004822530865 Combine like terms: 0.8472222222 + 0.00004822530865 = 0.84727044750865 0.00004822530865 + -0.01388888889x + x2 = 0.84727044750865 Factor a perfect square on the left side: (x + -0.006944444445)(x + -0.006944444445) = 0.84727044750865 Calculate the square root of the right side: 0.920472948 Break this problem into two subproblems by setting (x + -0.006944444445) equal to 0.920472948 and -0.920472948.Subproblem 1
x + -0.006944444445 = 0.920472948 Simplifying x + -0.006944444445 = 0.920472948 Reorder the terms: -0.006944444445 + x = 0.920472948 Solving -0.006944444445 + x = 0.920472948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = 0.920472948 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = 0.920472948 + 0.006944444445 x = 0.920472948 + 0.006944444445 Combine like terms: 0.920472948 + 0.006944444445 = 0.927417392445 x = 0.927417392445 Simplifying x = 0.927417392445Subproblem 2
x + -0.006944444445 = -0.920472948 Simplifying x + -0.006944444445 = -0.920472948 Reorder the terms: -0.006944444445 + x = -0.920472948 Solving -0.006944444445 + x = -0.920472948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = -0.920472948 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = -0.920472948 + 0.006944444445 x = -0.920472948 + 0.006944444445 Combine like terms: -0.920472948 + 0.006944444445 = -0.913528503555 x = -0.913528503555 Simplifying x = -0.913528503555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.927417392445, -0.913528503555}Solution
x = {0.927417392445, -0.913528503555}
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