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Simplifying 7x + -2 = 2(x + 1) * 5x + -4 Reorder the terms: -2 + 7x = 2(x + 1) * 5x + -4 Reorder the terms: -2 + 7x = 2(1 + x) * 5x + -4 Reorder the terms for easier multiplication: -2 + 7x = 2 * 5x(1 + x) + -4 Multiply 2 * 5 -2 + 7x = 10x(1 + x) + -4 -2 + 7x = (1 * 10x + x * 10x) + -4 -2 + 7x = (10x + 10x2) + -4 Reorder the terms: -2 + 7x = -4 + 10x + 10x2 Solving -2 + 7x = -4 + 10x + 10x2 Solving for variable 'x'. Reorder the terms: -2 + 4 + 7x + -10x + -10x2 = -4 + 10x + 10x2 + 4 + -10x + -10x2 Combine like terms: -2 + 4 = 2 2 + 7x + -10x + -10x2 = -4 + 10x + 10x2 + 4 + -10x + -10x2 Combine like terms: 7x + -10x = -3x 2 + -3x + -10x2 = -4 + 10x + 10x2 + 4 + -10x + -10x2 Reorder the terms: 2 + -3x + -10x2 = -4 + 4 + 10x + -10x + 10x2 + -10x2 Combine like terms: -4 + 4 = 0 2 + -3x + -10x2 = 0 + 10x + -10x + 10x2 + -10x2 2 + -3x + -10x2 = 10x + -10x + 10x2 + -10x2 Combine like terms: 10x + -10x = 0 2 + -3x + -10x2 = 0 + 10x2 + -10x2 2 + -3x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 2 + -3x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.2 + 0.3x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.3x + x2 = 0 + 0.2 0.3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.3x + x2 = 0.2 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 = 0.2 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.2 + 0.0225 Combine like terms: 0.2 + 0.0225 = 0.2225 0.0225 + 0.3x + x2 = 0.2225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.2225 Calculate the square root of the right side: 0.471699057 Break this problem into two subproblems by setting (x + 0.15) equal to 0.471699057 and -0.471699057.Subproblem 1
x + 0.15 = 0.471699057 Simplifying x + 0.15 = 0.471699057 Reorder the terms: 0.15 + x = 0.471699057 Solving 0.15 + x = 0.471699057 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 = 0.471699057 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.471699057 + -0.15 x = 0.471699057 + -0.15 Combine like terms: 0.471699057 + -0.15 = 0.321699057 x = 0.321699057 Simplifying x = 0.321699057Subproblem 2
x + 0.15 = -0.471699057 Simplifying x + 0.15 = -0.471699057 Reorder the terms: 0.15 + x = -0.471699057 Solving 0.15 + x = -0.471699057 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 = -0.471699057 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.471699057 + -0.15 x = -0.471699057 + -0.15 Combine like terms: -0.471699057 + -0.15 = -0.621699057 x = -0.621699057 Simplifying x = -0.621699057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.321699057, -0.621699057}
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