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Simplifying 7x + -2 = 5(x + 1) * 2x + -7 Reorder the terms: -2 + 7x = 5(x + 1) * 2x + -7 Reorder the terms: -2 + 7x = 5(1 + x) * 2x + -7 Reorder the terms for easier multiplication: -2 + 7x = 5 * 2x(1 + x) + -7 Multiply 5 * 2 -2 + 7x = 10x(1 + x) + -7 -2 + 7x = (1 * 10x + x * 10x) + -7 -2 + 7x = (10x + 10x2) + -7 Reorder the terms: -2 + 7x = -7 + 10x + 10x2 Solving -2 + 7x = -7 + 10x + 10x2 Solving for variable 'x'. Reorder the terms: -2 + 7 + 7x + -10x + -10x2 = -7 + 10x + 10x2 + 7 + -10x + -10x2 Combine like terms: -2 + 7 = 5 5 + 7x + -10x + -10x2 = -7 + 10x + 10x2 + 7 + -10x + -10x2 Combine like terms: 7x + -10x = -3x 5 + -3x + -10x2 = -7 + 10x + 10x2 + 7 + -10x + -10x2 Reorder the terms: 5 + -3x + -10x2 = -7 + 7 + 10x + -10x + 10x2 + -10x2 Combine like terms: -7 + 7 = 0 5 + -3x + -10x2 = 0 + 10x + -10x + 10x2 + -10x2 5 + -3x + -10x2 = 10x + -10x + 10x2 + -10x2 Combine like terms: 10x + -10x = 0 5 + -3x + -10x2 = 0 + 10x2 + -10x2 5 + -3x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 5 + -3x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.5 + 0.3x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.3x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.3x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.3x + x2 = 0 + 0.5 0.3x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.3x + x2 = 0.5 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.5 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.5 + 0.0225 Combine like terms: 0.5 + 0.0225 = 0.5225 0.0225 + 0.3x + x2 = 0.5225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (x + 0.15) equal to 0.722841615 and -0.722841615.Subproblem 1
x + 0.15 = 0.722841615 Simplifying x + 0.15 = 0.722841615 Reorder the terms: 0.15 + x = 0.722841615 Solving 0.15 + x = 0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.722841615 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.722841615 + -0.15 x = 0.722841615 + -0.15 Combine like terms: 0.722841615 + -0.15 = 0.572841615 x = 0.572841615 Simplifying x = 0.572841615Subproblem 2
x + 0.15 = -0.722841615 Simplifying x + 0.15 = -0.722841615 Reorder the terms: 0.15 + x = -0.722841615 Solving 0.15 + x = -0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.722841615 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.722841615 + -0.15 x = -0.722841615 + -0.15 Combine like terms: -0.722841615 + -0.15 = -0.872841615 x = -0.872841615 Simplifying x = -0.872841615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.572841615, -0.872841615}
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