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Simplifying (x + 5) * 2 + -1(3x + 8)(3x + -8) = 0 Reorder the terms: (5 + x) * 2 + -1(3x + 8)(3x + -8) = 0 Reorder the terms for easier multiplication: 2(5 + x) + -1(3x + 8)(3x + -8) = 0 (5 * 2 + x * 2) + -1(3x + 8)(3x + -8) = 0 (10 + 2x) + -1(3x + 8)(3x + -8) = 0 Reorder the terms: 10 + 2x + -1(8 + 3x)(3x + -8) = 0 Reorder the terms: 10 + 2x + -1(8 + 3x)(-8 + 3x) = 0 Multiply (8 + 3x) * (-8 + 3x) 10 + 2x + -1(8(-8 + 3x) + 3x * (-8 + 3x)) = 0 10 + 2x + -1((-8 * 8 + 3x * 8) + 3x * (-8 + 3x)) = 0 10 + 2x + -1((-64 + 24x) + 3x * (-8 + 3x)) = 0 10 + 2x + -1(-64 + 24x + (-8 * 3x + 3x * 3x)) = 0 10 + 2x + -1(-64 + 24x + (-24x + 9x2)) = 0 Combine like terms: 24x + -24x = 0 10 + 2x + -1(-64 + 0 + 9x2) = 0 10 + 2x + -1(-64 + 9x2) = 0 10 + 2x + (-64 * -1 + 9x2 * -1) = 0 10 + 2x + (64 + -9x2) = 0 Reorder the terms: 10 + 64 + 2x + -9x2 = 0 Combine like terms: 10 + 64 = 74 74 + 2x + -9x2 = 0 Solving 74 + 2x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -8.222222222 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '8.222222222' to each side of the equation. -8.222222222 + -0.2222222222x + 8.222222222 + x2 = 0 + 8.222222222 Reorder the terms: -8.222222222 + 8.222222222 + -0.2222222222x + x2 = 0 + 8.222222222 Combine like terms: -8.222222222 + 8.222222222 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 8.222222222 -0.2222222222x + x2 = 0 + 8.222222222 Combine like terms: 0 + 8.222222222 = 8.222222222 -0.2222222222x + x2 = 8.222222222 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 8.222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 8.222222222 + 0.01234567901 Combine like terms: 8.222222222 + 0.01234567901 = 8.23456790101 0.01234567901 + -0.2222222222x + x2 = 8.23456790101 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 8.23456790101 Calculate the square root of the right side: 2.869593682 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 2.869593682 and -2.869593682.Subproblem 1
x + -0.1111111111 = 2.869593682 Simplifying x + -0.1111111111 = 2.869593682 Reorder the terms: -0.1111111111 + x = 2.869593682 Solving -0.1111111111 + x = 2.869593682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 2.869593682 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 2.869593682 + 0.1111111111 x = 2.869593682 + 0.1111111111 Combine like terms: 2.869593682 + 0.1111111111 = 2.9807047931 x = 2.9807047931 Simplifying x = 2.9807047931Subproblem 2
x + -0.1111111111 = -2.869593682 Simplifying x + -0.1111111111 = -2.869593682 Reorder the terms: -0.1111111111 + x = -2.869593682 Solving -0.1111111111 + x = -2.869593682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -2.869593682 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -2.869593682 + 0.1111111111 x = -2.869593682 + 0.1111111111 Combine like terms: -2.869593682 + 0.1111111111 = -2.7584825709 x = -2.7584825709 Simplifying x = -2.7584825709Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9807047931, -2.7584825709}
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