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Simplifying (x + -0.2222)(x + 0.5) = 0 Reorder the terms: (-0.2222 + x)(x + 0.5) = 0 Reorder the terms: (-0.2222 + x)(0.5 + x) = 0 Multiply (-0.2222 + x) * (0.5 + x) (-0.2222(0.5 + x) + x(0.5 + x)) = 0 ((0.5 * -0.2222 + x * -0.2222) + x(0.5 + x)) = 0 ((-0.1111 + -0.2222x) + x(0.5 + x)) = 0 (-0.1111 + -0.2222x + (0.5 * x + x * x)) = 0 (-0.1111 + -0.2222x + (0.5x + x2)) = 0 Combine like terms: -0.2222x + 0.5x = 0.2778x (-0.1111 + 0.2778x + x2) = 0 Solving -0.1111 + 0.2778x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.1111' to each side of the equation. -0.1111 + 0.2778x + 0.1111 + x2 = 0 + 0.1111 Reorder the terms: -0.1111 + 0.1111 + 0.2778x + x2 = 0 + 0.1111 Combine like terms: -0.1111 + 0.1111 = 0.0000 0.0000 + 0.2778x + x2 = 0 + 0.1111 0.2778x + x2 = 0 + 0.1111 Combine like terms: 0 + 0.1111 = 0.1111 0.2778x + x2 = 0.1111 The x term is 0.2778x. Take half its coefficient (0.1389). Square it (0.01929321) and add it to both sides. Add '0.01929321' to each side of the equation. 0.2778x + 0.01929321 + x2 = 0.1111 + 0.01929321 Reorder the terms: 0.01929321 + 0.2778x + x2 = 0.1111 + 0.01929321 Combine like terms: 0.1111 + 0.01929321 = 0.13039321 0.01929321 + 0.2778x + x2 = 0.13039321 Factor a perfect square on the left side: (x + 0.1389)(x + 0.1389) = 0.13039321 Calculate the square root of the right side: 0.3611 Break this problem into two subproblems by setting (x + 0.1389) equal to 0.3611 and -0.3611.Subproblem 1
x + 0.1389 = 0.3611 Simplifying x + 0.1389 = 0.3611 Reorder the terms: 0.1389 + x = 0.3611 Solving 0.1389 + x = 0.3611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1389' to each side of the equation. 0.1389 + -0.1389 + x = 0.3611 + -0.1389 Combine like terms: 0.1389 + -0.1389 = 0.0000 0.0000 + x = 0.3611 + -0.1389 x = 0.3611 + -0.1389 Combine like terms: 0.3611 + -0.1389 = 0.2222 x = 0.2222 Simplifying x = 0.2222Subproblem 2
x + 0.1389 = -0.3611 Simplifying x + 0.1389 = -0.3611 Reorder the terms: 0.1389 + x = -0.3611 Solving 0.1389 + x = -0.3611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1389' to each side of the equation. 0.1389 + -0.1389 + x = -0.3611 + -0.1389 Combine like terms: 0.1389 + -0.1389 = 0.0000 0.0000 + x = -0.3611 + -0.1389 x = -0.3611 + -0.1389 Combine like terms: -0.3611 + -0.1389 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2222, -0.5}
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