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Simplifying 36x2 + 26x + -47 = 0 Reorder the terms: -47 + 26x + 36x2 = 0 Solving -47 + 26x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.305555556 + 0.7222222222x + x2 = 0 Move the constant term to the right: Add '1.305555556' to each side of the equation. -1.305555556 + 0.7222222222x + 1.305555556 + x2 = 0 + 1.305555556 Reorder the terms: -1.305555556 + 1.305555556 + 0.7222222222x + x2 = 0 + 1.305555556 Combine like terms: -1.305555556 + 1.305555556 = 0.000000000 0.000000000 + 0.7222222222x + x2 = 0 + 1.305555556 0.7222222222x + x2 = 0 + 1.305555556 Combine like terms: 0 + 1.305555556 = 1.305555556 0.7222222222x + x2 = 1.305555556 The x term is 0.7222222222x. Take half its coefficient (0.3611111111). Square it (0.1304012346) and add it to both sides. Add '0.1304012346' to each side of the equation. 0.7222222222x + 0.1304012346 + x2 = 1.305555556 + 0.1304012346 Reorder the terms: 0.1304012346 + 0.7222222222x + x2 = 1.305555556 + 0.1304012346 Combine like terms: 1.305555556 + 0.1304012346 = 1.4359567906 0.1304012346 + 0.7222222222x + x2 = 1.4359567906 Factor a perfect square on the left side: (x + 0.3611111111)(x + 0.3611111111) = 1.4359567906 Calculate the square root of the right side: 1.198314145 Break this problem into two subproblems by setting (x + 0.3611111111) equal to 1.198314145 and -1.198314145.Subproblem 1
x + 0.3611111111 = 1.198314145 Simplifying x + 0.3611111111 = 1.198314145 Reorder the terms: 0.3611111111 + x = 1.198314145 Solving 0.3611111111 + x = 1.198314145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3611111111' to each side of the equation. 0.3611111111 + -0.3611111111 + x = 1.198314145 + -0.3611111111 Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000 0.0000000000 + x = 1.198314145 + -0.3611111111 x = 1.198314145 + -0.3611111111 Combine like terms: 1.198314145 + -0.3611111111 = 0.8372030339 x = 0.8372030339 Simplifying x = 0.8372030339Subproblem 2
x + 0.3611111111 = -1.198314145 Simplifying x + 0.3611111111 = -1.198314145 Reorder the terms: 0.3611111111 + x = -1.198314145 Solving 0.3611111111 + x = -1.198314145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3611111111' to each side of the equation. 0.3611111111 + -0.3611111111 + x = -1.198314145 + -0.3611111111 Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000 0.0000000000 + x = -1.198314145 + -0.3611111111 x = -1.198314145 + -0.3611111111 Combine like terms: -1.198314145 + -0.3611111111 = -1.5594252561 x = -1.5594252561 Simplifying x = -1.5594252561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8372030339, -1.5594252561}
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