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Simplifying 36x2 + 94x + -10 = 0 Reorder the terms: -10 + 94x + 36x2 = 0 Solving -10 + 94x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 47x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 47x + 18x2)' equal to zero and attempt to solve: Simplifying -5 + 47x + 18x2 = 0 Solving -5 + 47x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + 2.611111111x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 2.611111111x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 2.611111111x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 2.611111111x + x2 = 0 + 0.2777777778 2.611111111x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 2.611111111x + x2 = 0.2777777778 The x term is 2.611111111x. Take half its coefficient (1.305555556). Square it (1.704475310) and add it to both sides. Add '1.704475310' to each side of the equation. 2.611111111x + 1.704475310 + x2 = 0.2777777778 + 1.704475310 Reorder the terms: 1.704475310 + 2.611111111x + x2 = 0.2777777778 + 1.704475310 Combine like terms: 0.2777777778 + 1.704475310 = 1.9822530878 1.704475310 + 2.611111111x + x2 = 1.9822530878 Factor a perfect square on the left side: (x + 1.305555556)(x + 1.305555556) = 1.9822530878 Calculate the square root of the right side: 1.4079251 Break this problem into two subproblems by setting (x + 1.305555556) equal to 1.4079251 and -1.4079251.Subproblem 1
x + 1.305555556 = 1.4079251 Simplifying x + 1.305555556 = 1.4079251 Reorder the terms: 1.305555556 + x = 1.4079251 Solving 1.305555556 + x = 1.4079251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.305555556' to each side of the equation. 1.305555556 + -1.305555556 + x = 1.4079251 + -1.305555556 Combine like terms: 1.305555556 + -1.305555556 = 0.000000000 0.000000000 + x = 1.4079251 + -1.305555556 x = 1.4079251 + -1.305555556 Combine like terms: 1.4079251 + -1.305555556 = 0.102369544 x = 0.102369544 Simplifying x = 0.102369544Subproblem 2
x + 1.305555556 = -1.4079251 Simplifying x + 1.305555556 = -1.4079251 Reorder the terms: 1.305555556 + x = -1.4079251 Solving 1.305555556 + x = -1.4079251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.305555556' to each side of the equation. 1.305555556 + -1.305555556 + x = -1.4079251 + -1.305555556 Combine like terms: 1.305555556 + -1.305555556 = 0.000000000 0.000000000 + x = -1.4079251 + -1.305555556 x = -1.4079251 + -1.305555556 Combine like terms: -1.4079251 + -1.305555556 = -2.713480656 x = -2.713480656 Simplifying x = -2.713480656Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.102369544, -2.713480656}Solution
x = {0.102369544, -2.713480656}
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