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Simplifying 5x2 + 11x + -66 = 0 Reorder the terms: -66 + 11x + 5x2 = 0 Solving -66 + 11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -13.2 + 2.2x + x2 = 0 Move the constant term to the right: Add '13.2' to each side of the equation. -13.2 + 2.2x + 13.2 + x2 = 0 + 13.2 Reorder the terms: -13.2 + 13.2 + 2.2x + x2 = 0 + 13.2 Combine like terms: -13.2 + 13.2 = 0.0 0.0 + 2.2x + x2 = 0 + 13.2 2.2x + x2 = 0 + 13.2 Combine like terms: 0 + 13.2 = 13.2 2.2x + x2 = 13.2 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 13.2 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 13.2 + 1.21 Combine like terms: 13.2 + 1.21 = 14.41 1.21 + 2.2x + x2 = 14.41 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 14.41 Calculate the square root of the right side: 3.796050579 Break this problem into two subproblems by setting (x + 1.1) equal to 3.796050579 and -3.796050579.Subproblem 1
x + 1.1 = 3.796050579 Simplifying x + 1.1 = 3.796050579 Reorder the terms: 1.1 + x = 3.796050579 Solving 1.1 + x = 3.796050579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 3.796050579 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 3.796050579 + -1.1 x = 3.796050579 + -1.1 Combine like terms: 3.796050579 + -1.1 = 2.696050579 x = 2.696050579 Simplifying x = 2.696050579Subproblem 2
x + 1.1 = -3.796050579 Simplifying x + 1.1 = -3.796050579 Reorder the terms: 1.1 + x = -3.796050579 Solving 1.1 + x = -3.796050579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -3.796050579 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -3.796050579 + -1.1 x = -3.796050579 + -1.1 Combine like terms: -3.796050579 + -1.1 = -4.896050579 x = -4.896050579 Simplifying x = -4.896050579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.696050579, -4.896050579}
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