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Simplifying 11x + -5 = 4 + -5x2 Reorder the terms: -5 + 11x = 4 + -5x2 Solving -5 + 11x = 4 + -5x2 Solving for variable 'x'. Reorder the terms: -5 + -4 + 11x + 5x2 = 4 + -5x2 + -4 + 5x2 Combine like terms: -5 + -4 = -9 -9 + 11x + 5x2 = 4 + -5x2 + -4 + 5x2 Reorder the terms: -9 + 11x + 5x2 = 4 + -4 + -5x2 + 5x2 Combine like terms: 4 + -4 = 0 -9 + 11x + 5x2 = 0 + -5x2 + 5x2 -9 + 11x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -9 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 2.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 2.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 2.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 2.2x + x2 = 0 + 1.8 2.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 2.2x + x2 = 1.8 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 = 1.8 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 1.8 + 1.21 Combine like terms: 1.8 + 1.21 = 3.01 1.21 + 2.2x + x2 = 3.01 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + 1.1) equal to 1.734935157 and -1.734935157.Subproblem 1
x + 1.1 = 1.734935157 Simplifying x + 1.1 = 1.734935157 Reorder the terms: 1.1 + x = 1.734935157 Solving 1.1 + x = 1.734935157 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 = 1.734935157 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.734935157 + -1.1 x = 1.734935157 + -1.1 Combine like terms: 1.734935157 + -1.1 = 0.634935157 x = 0.634935157 Simplifying x = 0.634935157Subproblem 2
x + 1.1 = -1.734935157 Simplifying x + 1.1 = -1.734935157 Reorder the terms: 1.1 + x = -1.734935157 Solving 1.1 + x = -1.734935157 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 = -1.734935157 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.734935157 + -1.1 x = -1.734935157 + -1.1 Combine like terms: -1.734935157 + -1.1 = -2.834935157 x = -2.834935157 Simplifying x = -2.834935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.634935157, -2.834935157}
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