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Simplifying -5(x + -1) * x = 6x + -11 Reorder the terms: -5(-1 + x) * x = 6x + -11 Reorder the terms for easier multiplication: -5x(-1 + x) = 6x + -11 (-1 * -5x + x * -5x) = 6x + -11 (5x + -5x2) = 6x + -11 Reorder the terms: 5x + -5x2 = -11 + 6x Solving 5x + -5x2 = -11 + 6x Solving for variable 'x'. Reorder the terms: 11 + 5x + -6x + -5x2 = -11 + 6x + 11 + -6x Combine like terms: 5x + -6x = -1x 11 + -1x + -5x2 = -11 + 6x + 11 + -6x Reorder the terms: 11 + -1x + -5x2 = -11 + 11 + 6x + -6x Combine like terms: -11 + 11 = 0 11 + -1x + -5x2 = 0 + 6x + -6x 11 + -1x + -5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 11 + -1x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.2 + 0.2x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.2x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.2x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.2x + x2 = 0 + 2.2 0.2x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.2x + x2 = 2.2 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 2.2 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 2.2 + 0.01 Combine like terms: 2.2 + 0.01 = 2.21 0.01 + 0.2x + x2 = 2.21 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (x + 0.1) equal to 1.486606875 and -1.486606875.Subproblem 1
x + 0.1 = 1.486606875 Simplifying x + 0.1 = 1.486606875 Reorder the terms: 0.1 + x = 1.486606875 Solving 0.1 + x = 1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.486606875 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.486606875 + -0.1 x = 1.486606875 + -0.1 Combine like terms: 1.486606875 + -0.1 = 1.386606875 x = 1.386606875 Simplifying x = 1.386606875Subproblem 2
x + 0.1 = -1.486606875 Simplifying x + 0.1 = -1.486606875 Reorder the terms: 0.1 + x = -1.486606875 Solving 0.1 + x = -1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.486606875 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.486606875 + -0.1 x = -1.486606875 + -0.1 Combine like terms: -1.486606875 + -0.1 = -1.586606875 x = -1.586606875 Simplifying x = -1.586606875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.386606875, -1.586606875}
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