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Simplifying 5x2 + 11x + -35 = 0 Reorder the terms: -35 + 11x + 5x2 = 0 Solving -35 + 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'. -7 + 2.2x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2.2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 2.2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2.2x + x2 = 0 + 7 2.2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 2.2x + x2 = 7 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 = 7 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 7 + 1.21 Combine like terms: 7 + 1.21 = 8.21 1.21 + 2.2x + x2 = 8.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 8.21 Calculate the square root of the right side: 2.865309756 Break this problem into two subproblems by setting (x + 1.1) equal to 2.865309756 and -2.865309756.Subproblem 1
x + 1.1 = 2.865309756 Simplifying x + 1.1 = 2.865309756 Reorder the terms: 1.1 + x = 2.865309756 Solving 1.1 + x = 2.865309756 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 = 2.865309756 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.865309756 + -1.1 x = 2.865309756 + -1.1 Combine like terms: 2.865309756 + -1.1 = 1.765309756 x = 1.765309756 Simplifying x = 1.765309756Subproblem 2
x + 1.1 = -2.865309756 Simplifying x + 1.1 = -2.865309756 Reorder the terms: 1.1 + x = -2.865309756 Solving 1.1 + x = -2.865309756 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 = -2.865309756 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.865309756 + -1.1 x = -2.865309756 + -1.1 Combine like terms: -2.865309756 + -1.1 = -3.965309756 x = -3.965309756 Simplifying x = -3.965309756Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.765309756, -3.965309756}
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