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Simplifying 36x2 + -25x + -16 = 0 Reorder the terms: -16 + -25x + 36x2 = 0 Solving -16 + -25x + 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'. -0.4444444444 + -0.6944444444x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.6944444444x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.6944444444x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.6944444444x + x2 = 0 + 0.4444444444 -0.6944444444x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.6944444444x + x2 = 0.4444444444 The x term is -0.6944444444x. Take half its coefficient (-0.3472222222). Square it (0.1205632716) and add it to both sides. Add '0.1205632716' to each side of the equation. -0.6944444444x + 0.1205632716 + x2 = 0.4444444444 + 0.1205632716 Reorder the terms: 0.1205632716 + -0.6944444444x + x2 = 0.4444444444 + 0.1205632716 Combine like terms: 0.4444444444 + 0.1205632716 = 0.565007716 0.1205632716 + -0.6944444444x + x2 = 0.565007716 Factor a perfect square on the left side: (x + -0.3472222222)(x + -0.3472222222) = 0.565007716 Calculate the square root of the right side: 0.751669952 Break this problem into two subproblems by setting (x + -0.3472222222) equal to 0.751669952 and -0.751669952.Subproblem 1
x + -0.3472222222 = 0.751669952 Simplifying x + -0.3472222222 = 0.751669952 Reorder the terms: -0.3472222222 + x = 0.751669952 Solving -0.3472222222 + x = 0.751669952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3472222222' to each side of the equation. -0.3472222222 + 0.3472222222 + x = 0.751669952 + 0.3472222222 Combine like terms: -0.3472222222 + 0.3472222222 = 0.0000000000 0.0000000000 + x = 0.751669952 + 0.3472222222 x = 0.751669952 + 0.3472222222 Combine like terms: 0.751669952 + 0.3472222222 = 1.0988921742 x = 1.0988921742 Simplifying x = 1.0988921742Subproblem 2
x + -0.3472222222 = -0.751669952 Simplifying x + -0.3472222222 = -0.751669952 Reorder the terms: -0.3472222222 + x = -0.751669952 Solving -0.3472222222 + x = -0.751669952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3472222222' to each side of the equation. -0.3472222222 + 0.3472222222 + x = -0.751669952 + 0.3472222222 Combine like terms: -0.3472222222 + 0.3472222222 = 0.0000000000 0.0000000000 + x = -0.751669952 + 0.3472222222 x = -0.751669952 + 0.3472222222 Combine like terms: -0.751669952 + 0.3472222222 = -0.4044477298 x = -0.4044477298 Simplifying x = -0.4044477298Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0988921742, -0.4044477298}
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