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Simplifying 9x2 + 62x + -27 = 0 Reorder the terms: -27 + 62x + 9x2 = 0 Solving -27 + 62x + 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'. -3 + 6.888888889x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6.888888889x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6.888888889x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6.888888889x + x2 = 0 + 3 6.888888889x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6.888888889x + x2 = 3 The x term is 6.888888889x. Take half its coefficient (3.444444445). Square it (11.86419753) and add it to both sides. Add '11.86419753' to each side of the equation. 6.888888889x + 11.86419753 + x2 = 3 + 11.86419753 Reorder the terms: 11.86419753 + 6.888888889x + x2 = 3 + 11.86419753 Combine like terms: 3 + 11.86419753 = 14.86419753 11.86419753 + 6.888888889x + x2 = 14.86419753 Factor a perfect square on the left side: (x + 3.444444445)(x + 3.444444445) = 14.86419753 Calculate the square root of the right side: 3.855411461 Break this problem into two subproblems by setting (x + 3.444444445) equal to 3.855411461 and -3.855411461.Subproblem 1
x + 3.444444445 = 3.855411461 Simplifying x + 3.444444445 = 3.855411461 Reorder the terms: 3.444444445 + x = 3.855411461 Solving 3.444444445 + x = 3.855411461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = 3.855411461 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = 3.855411461 + -3.444444445 x = 3.855411461 + -3.444444445 Combine like terms: 3.855411461 + -3.444444445 = 0.410967016 x = 0.410967016 Simplifying x = 0.410967016Subproblem 2
x + 3.444444445 = -3.855411461 Simplifying x + 3.444444445 = -3.855411461 Reorder the terms: 3.444444445 + x = -3.855411461 Solving 3.444444445 + x = -3.855411461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = -3.855411461 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = -3.855411461 + -3.444444445 x = -3.855411461 + -3.444444445 Combine like terms: -3.855411461 + -3.444444445 = -7.299855906 x = -7.299855906 Simplifying x = -7.299855906Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.410967016, -7.299855906}
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