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Simplifying 5x(x + 1) + -3(x + -2) = 17 Reorder the terms: 5x(1 + x) + -3(x + -2) = 17 (1 * 5x + x * 5x) + -3(x + -2) = 17 (5x + 5x2) + -3(x + -2) = 17 Reorder the terms: 5x + 5x2 + -3(-2 + x) = 17 5x + 5x2 + (-2 * -3 + x * -3) = 17 5x + 5x2 + (6 + -3x) = 17 Reorder the terms: 6 + 5x + -3x + 5x2 = 17 Combine like terms: 5x + -3x = 2x 6 + 2x + 5x2 = 17 Solving 6 + 2x + 5x2 = 17 Solving for variable 'x'. Reorder the terms: 6 + -17 + 2x + 5x2 = 17 + -17 Combine like terms: 6 + -17 = -11 -11 + 2x + 5x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -11 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.4x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.4x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.4x + x2 = 0 + 2.2 0.4x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.4x + x2 = 2.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 2.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 2.2 + 0.04 Combine like terms: 2.2 + 0.04 = 2.24 0.04 + 0.4x + x2 = 2.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (x + 0.2) equal to 1.496662955 and -1.496662955.Subproblem 1
x + 0.2 = 1.496662955 Simplifying x + 0.2 = 1.496662955 Reorder the terms: 0.2 + x = 1.496662955 Solving 0.2 + x = 1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.496662955 + -0.2 x = 1.496662955 + -0.2 Combine like terms: 1.496662955 + -0.2 = 1.296662955 x = 1.296662955 Simplifying x = 1.296662955Subproblem 2
x + 0.2 = -1.496662955 Simplifying x + 0.2 = -1.496662955 Reorder the terms: 0.2 + x = -1.496662955 Solving 0.2 + x = -1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.496662955 + -0.2 x = -1.496662955 + -0.2 Combine like terms: -1.496662955 + -0.2 = -1.696662955 x = -1.696662955 Simplifying x = -1.696662955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296662955, -1.696662955}
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