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Simplifying x(5x + 7) = 7 Reorder the terms: x(7 + 5x) = 7 (7 * x + 5x * x) = 7 (7x + 5x2) = 7 Solving 7x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 7x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 1.4x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 1.4x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 1.4x + x2 = 0 + 1.4 1.4x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 1.4x + x2 = 1.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 1.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 1.4 + 0.49 Combine like terms: 1.4 + 0.49 = 1.89 0.49 + 1.4x + x2 = 1.89 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (x + 0.7) equal to 1.374772708 and -1.374772708.Subproblem 1
x + 0.7 = 1.374772708 Simplifying x + 0.7 = 1.374772708 Reorder the terms: 0.7 + x = 1.374772708 Solving 0.7 + x = 1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 1.374772708 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.374772708 + -0.7 x = 1.374772708 + -0.7 Combine like terms: 1.374772708 + -0.7 = 0.674772708 x = 0.674772708 Simplifying x = 0.674772708Subproblem 2
x + 0.7 = -1.374772708 Simplifying x + 0.7 = -1.374772708 Reorder the terms: 0.7 + x = -1.374772708 Solving 0.7 + x = -1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -1.374772708 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.374772708 + -0.7 x = -1.374772708 + -0.7 Combine like terms: -1.374772708 + -0.7 = -2.074772708 x = -2.074772708 Simplifying x = -2.074772708Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.674772708, -2.074772708}
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