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Simplifying (7x + 8) + -1(-3x)(-3x) + -5x + 8 = 0 Reorder the terms: (8 + 7x) + -1(-3x)(-3x) + -5x + 8 = 0 Remove parenthesis around (8 + 7x) 8 + 7x + -1(-3x)(-3x) + -5x + 8 = 0 Remove parenthesis around (-3x) 8 + 7x + -1 * -3x(-3x) + -5x + 8 = 0 Remove parenthesis around (-3x) 8 + 7x + -1 * -3x * -3x + -5x + 8 = 0 Reorder the terms for easier multiplication: 8 + 7x + -1 * -3 * -3x * x + -5x + 8 = 0 Multiply -1 * -3 8 + 7x + 3 * -3x * x + -5x + 8 = 0 Multiply 3 * -3 8 + 7x + -9x * x + -5x + 8 = 0 Multiply x * x 8 + 7x + -9x2 + -5x + 8 = 0 Reorder the terms: 8 + 8 + 7x + -5x + -9x2 = 0 Combine like terms: 8 + 8 = 16 16 + 7x + -5x + -9x2 = 0 Combine like terms: 7x + -5x = 2x 16 + 2x + -9x2 = 0 Solving 16 + 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'. -1.777777778 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.2222222222x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.2222222222x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 1.777777778 -0.2222222222x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.2222222222x + x2 = 1.777777778 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 = 1.777777778 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 1.777777778 + 0.01234567901 Combine like terms: 1.777777778 + 0.01234567901 = 1.79012345701 0.01234567901 + -0.2222222222x + x2 = 1.79012345701 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 1.79012345701 Calculate the square root of the right side: 1.337954953 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.337954953 and -1.337954953.Subproblem 1
x + -0.1111111111 = 1.337954953 Simplifying x + -0.1111111111 = 1.337954953 Reorder the terms: -0.1111111111 + x = 1.337954953 Solving -0.1111111111 + x = 1.337954953 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 = 1.337954953 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.337954953 + 0.1111111111 x = 1.337954953 + 0.1111111111 Combine like terms: 1.337954953 + 0.1111111111 = 1.4490660641 x = 1.4490660641 Simplifying x = 1.4490660641Subproblem 2
x + -0.1111111111 = -1.337954953 Simplifying x + -0.1111111111 = -1.337954953 Reorder the terms: -0.1111111111 + x = -1.337954953 Solving -0.1111111111 + x = -1.337954953 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 = -1.337954953 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.337954953 + 0.1111111111 x = -1.337954953 + 0.1111111111 Combine like terms: -1.337954953 + 0.1111111111 = -1.2268438419 x = -1.2268438419 Simplifying x = -1.2268438419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4490660641, -1.2268438419}
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