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Simplifying 5x2 + 6x + 7x = 2(x + 2) Reorder the terms: 6x + 7x + 5x2 = 2(x + 2) Combine like terms: 6x + 7x = 13x 13x + 5x2 = 2(x + 2) Reorder the terms: 13x + 5x2 = 2(2 + x) 13x + 5x2 = (2 * 2 + x * 2) 13x + 5x2 = (4 + 2x) Solving 13x + 5x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -4 + 13x + -2x + 5x2 = 4 + 2x + -4 + -2x Combine like terms: 13x + -2x = 11x -4 + 11x + 5x2 = 4 + 2x + -4 + -2x Reorder the terms: -4 + 11x + 5x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -4 + 11x + 5x2 = 0 + 2x + -2x -4 + 11x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 2.2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 2.2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 2.2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 2.2x + x2 = 0 + 0.8 2.2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 2.2x + x2 = 0.8 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 = 0.8 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 0.8 + 1.21 Combine like terms: 0.8 + 1.21 = 2.01 1.21 + 2.2x + x2 = 2.01 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 2.01 Calculate the square root of the right side: 1.417744688 Break this problem into two subproblems by setting (x + 1.1) equal to 1.417744688 and -1.417744688.Subproblem 1
x + 1.1 = 1.417744688 Simplifying x + 1.1 = 1.417744688 Reorder the terms: 1.1 + x = 1.417744688 Solving 1.1 + x = 1.417744688 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 = 1.417744688 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.417744688 + -1.1 x = 1.417744688 + -1.1 Combine like terms: 1.417744688 + -1.1 = 0.317744688 x = 0.317744688 Simplifying x = 0.317744688Subproblem 2
x + 1.1 = -1.417744688 Simplifying x + 1.1 = -1.417744688 Reorder the terms: 1.1 + x = -1.417744688 Solving 1.1 + x = -1.417744688 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 = -1.417744688 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.417744688 + -1.1 x = -1.417744688 + -1.1 Combine like terms: -1.417744688 + -1.1 = -2.517744688 x = -2.517744688 Simplifying x = -2.517744688Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.317744688, -2.517744688}
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