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Simplifying (9x2 + 5x + 7) + (3x + 9x) = 0 Reorder the terms: (7 + 5x + 9x2) + (3x + 9x) = 0 Remove parenthesis around (7 + 5x + 9x2) 7 + 5x + 9x2 + (3x + 9x) = 0 Combine like terms: 3x + 9x = 12x 7 + 5x + 9x2 + (12x) = 0 7 + 5x + 9x2 + (12x) = 0 Reorder the terms: 7 + 5x + (12x) + 9x2 = 0 Combine like terms: 5x + (12x) = 17x 7 + 17x + 9x2 = 0 Solving 7 + 17x + 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'. 0.7777777778 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 1.888888889x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 1.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 1.888888889x + x2 = 0 + -0.7777777778 1.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 1.888888889x + x2 = -0.7777777778 The x term is 1.888888889x. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889x + 0.8919753087 + x2 = -0.7777777778 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = -0.7777777778 + 0.8919753087 Combine like terms: -0.7777777778 + 0.8919753087 = 0.1141975309 0.8919753087 + 1.888888889x + x2 = 0.1141975309 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 0.1141975309 Calculate the square root of the right side: 0.337931252 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 0.337931252 and -0.337931252.Subproblem 1
x + 0.9444444445 = 0.337931252 Simplifying x + 0.9444444445 = 0.337931252 Reorder the terms: 0.9444444445 + x = 0.337931252 Solving 0.9444444445 + x = 0.337931252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 0.337931252 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 0.337931252 + -0.9444444445 x = 0.337931252 + -0.9444444445 Combine like terms: 0.337931252 + -0.9444444445 = -0.6065131925 x = -0.6065131925 Simplifying x = -0.6065131925Subproblem 2
x + 0.9444444445 = -0.337931252 Simplifying x + 0.9444444445 = -0.337931252 Reorder the terms: 0.9444444445 + x = -0.337931252 Solving 0.9444444445 + x = -0.337931252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -0.337931252 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -0.337931252 + -0.9444444445 x = -0.337931252 + -0.9444444445 Combine like terms: -0.337931252 + -0.9444444445 = -1.2823756965 x = -1.2823756965 Simplifying x = -1.2823756965Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.6065131925, -1.2823756965}
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