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Simplifying 26 + -6x = -1 + 5x(x + 1) Reorder the terms: 26 + -6x = -1 + 5x(1 + x) 26 + -6x = -1 + (1 * 5x + x * 5x) 26 + -6x = -1 + (5x + 5x2) Solving 26 + -6x = -1 + 5x + 5x2 Solving for variable 'x'. Reorder the terms: 26 + 1 + -6x + -5x + -5x2 = -1 + 5x + 5x2 + 1 + -5x + -5x2 Combine like terms: 26 + 1 = 27 27 + -6x + -5x + -5x2 = -1 + 5x + 5x2 + 1 + -5x + -5x2 Combine like terms: -6x + -5x = -11x 27 + -11x + -5x2 = -1 + 5x + 5x2 + 1 + -5x + -5x2 Reorder the terms: 27 + -11x + -5x2 = -1 + 1 + 5x + -5x + 5x2 + -5x2 Combine like terms: -1 + 1 = 0 27 + -11x + -5x2 = 0 + 5x + -5x + 5x2 + -5x2 27 + -11x + -5x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 27 + -11x + -5x2 = 0 + 5x2 + -5x2 27 + -11x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 27 + -11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.4 + 2.2x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 2.2x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 2.2x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 2.2x + x2 = 0 + 5.4 2.2x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 2.2x + x2 = 5.4 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 = 5.4 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 5.4 + 1.21 Combine like terms: 5.4 + 1.21 = 6.61 1.21 + 2.2x + x2 = 6.61 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 6.61 Calculate the square root of the right side: 2.570992026 Break this problem into two subproblems by setting (x + 1.1) equal to 2.570992026 and -2.570992026.Subproblem 1
x + 1.1 = 2.570992026 Simplifying x + 1.1 = 2.570992026 Reorder the terms: 1.1 + x = 2.570992026 Solving 1.1 + x = 2.570992026 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 = 2.570992026 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.570992026 + -1.1 x = 2.570992026 + -1.1 Combine like terms: 2.570992026 + -1.1 = 1.470992026 x = 1.470992026 Simplifying x = 1.470992026Subproblem 2
x + 1.1 = -2.570992026 Simplifying x + 1.1 = -2.570992026 Reorder the terms: 1.1 + x = -2.570992026 Solving 1.1 + x = -2.570992026 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 = -2.570992026 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.570992026 + -1.1 x = -2.570992026 + -1.1 Combine like terms: -2.570992026 + -1.1 = -3.670992026 x = -3.670992026 Simplifying x = -3.670992026Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.470992026, -3.670992026}
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