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Simplifying 72x2 + 7x + -4 = 0 Reorder the terms: -4 + 7x + 72x2 = 0 Solving -4 + 7x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.05555555556 + 0.09722222222x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.09722222222x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.09722222222x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.09722222222x + x2 = 0 + 0.05555555556 0.09722222222x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.09722222222x + x2 = 0.05555555556 The x term is 0.09722222222x. Take half its coefficient (0.04861111111). Square it (0.002363040123) and add it to both sides. Add '0.002363040123' to each side of the equation. 0.09722222222x + 0.002363040123 + x2 = 0.05555555556 + 0.002363040123 Reorder the terms: 0.002363040123 + 0.09722222222x + x2 = 0.05555555556 + 0.002363040123 Combine like terms: 0.05555555556 + 0.002363040123 = 0.057918595683 0.002363040123 + 0.09722222222x + x2 = 0.057918595683 Factor a perfect square on the left side: (x + 0.04861111111)(x + 0.04861111111) = 0.057918595683 Calculate the square root of the right side: 0.240662826 Break this problem into two subproblems by setting (x + 0.04861111111) equal to 0.240662826 and -0.240662826.Subproblem 1
x + 0.04861111111 = 0.240662826 Simplifying x + 0.04861111111 = 0.240662826 Reorder the terms: 0.04861111111 + x = 0.240662826 Solving 0.04861111111 + x = 0.240662826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04861111111' to each side of the equation. 0.04861111111 + -0.04861111111 + x = 0.240662826 + -0.04861111111 Combine like terms: 0.04861111111 + -0.04861111111 = 0.00000000000 0.00000000000 + x = 0.240662826 + -0.04861111111 x = 0.240662826 + -0.04861111111 Combine like terms: 0.240662826 + -0.04861111111 = 0.19205171489 x = 0.19205171489 Simplifying x = 0.19205171489Subproblem 2
x + 0.04861111111 = -0.240662826 Simplifying x + 0.04861111111 = -0.240662826 Reorder the terms: 0.04861111111 + x = -0.240662826 Solving 0.04861111111 + x = -0.240662826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04861111111' to each side of the equation. 0.04861111111 + -0.04861111111 + x = -0.240662826 + -0.04861111111 Combine like terms: 0.04861111111 + -0.04861111111 = 0.00000000000 0.00000000000 + x = -0.240662826 + -0.04861111111 x = -0.240662826 + -0.04861111111 Combine like terms: -0.240662826 + -0.04861111111 = -0.28927393711 x = -0.28927393711 Simplifying x = -0.28927393711Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19205171489, -0.28927393711}
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