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Simplifying (-1x + 7) * x + 5x(9x + 8) + -7 = 0 Reorder the terms: (7 + -1x) * x + 5x(9x + 8) + -7 = 0 Reorder the terms for easier multiplication: x(7 + -1x) + 5x(9x + 8) + -7 = 0 (7 * x + -1x * x) + 5x(9x + 8) + -7 = 0 (7x + -1x2) + 5x(9x + 8) + -7 = 0 Reorder the terms: 7x + -1x2 + 5x(8 + 9x) + -7 = 0 7x + -1x2 + (8 * 5x + 9x * 5x) + -7 = 0 7x + -1x2 + (40x + 45x2) + -7 = 0 Reorder the terms: -7 + 7x + 40x + -1x2 + 45x2 = 0 Combine like terms: 7x + 40x = 47x -7 + 47x + -1x2 + 45x2 = 0 Combine like terms: -1x2 + 45x2 = 44x2 -7 + 47x + 44x2 = 0 Solving -7 + 47x + 44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.1590909091 + 1.068181818x + x2 = 0 Move the constant term to the right: Add '0.1590909091' to each side of the equation. -0.1590909091 + 1.068181818x + 0.1590909091 + x2 = 0 + 0.1590909091 Reorder the terms: -0.1590909091 + 0.1590909091 + 1.068181818x + x2 = 0 + 0.1590909091 Combine like terms: -0.1590909091 + 0.1590909091 = 0.0000000000 0.0000000000 + 1.068181818x + x2 = 0 + 0.1590909091 1.068181818x + x2 = 0 + 0.1590909091 Combine like terms: 0 + 0.1590909091 = 0.1590909091 1.068181818x + x2 = 0.1590909091 The x term is 1.068181818x. Take half its coefficient (0.534090909). Square it (0.2852530991) and add it to both sides. Add '0.2852530991' to each side of the equation. 1.068181818x + 0.2852530991 + x2 = 0.1590909091 + 0.2852530991 Reorder the terms: 0.2852530991 + 1.068181818x + x2 = 0.1590909091 + 0.2852530991 Combine like terms: 0.1590909091 + 0.2852530991 = 0.4443440082 0.2852530991 + 1.068181818x + x2 = 0.4443440082 Factor a perfect square on the left side: (x + 0.534090909)(x + 0.534090909) = 0.4443440082 Calculate the square root of the right side: 0.666591335 Break this problem into two subproblems by setting (x + 0.534090909) equal to 0.666591335 and -0.666591335.Subproblem 1
x + 0.534090909 = 0.666591335 Simplifying x + 0.534090909 = 0.666591335 Reorder the terms: 0.534090909 + x = 0.666591335 Solving 0.534090909 + x = 0.666591335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.534090909' to each side of the equation. 0.534090909 + -0.534090909 + x = 0.666591335 + -0.534090909 Combine like terms: 0.534090909 + -0.534090909 = 0.000000000 0.000000000 + x = 0.666591335 + -0.534090909 x = 0.666591335 + -0.534090909 Combine like terms: 0.666591335 + -0.534090909 = 0.132500426 x = 0.132500426 Simplifying x = 0.132500426Subproblem 2
x + 0.534090909 = -0.666591335 Simplifying x + 0.534090909 = -0.666591335 Reorder the terms: 0.534090909 + x = -0.666591335 Solving 0.534090909 + x = -0.666591335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.534090909' to each side of the equation. 0.534090909 + -0.534090909 + x = -0.666591335 + -0.534090909 Combine like terms: 0.534090909 + -0.534090909 = 0.000000000 0.000000000 + x = -0.666591335 + -0.534090909 x = -0.666591335 + -0.534090909 Combine like terms: -0.666591335 + -0.534090909 = -1.200682244 x = -1.200682244 Simplifying x = -1.200682244Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.132500426, -1.200682244}
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