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Simplifying 6(5x + 7) * 4x + -10 = 7 Reorder the terms: 6(7 + 5x) * 4x + -10 = 7 Reorder the terms for easier multiplication: 6 * 4x(7 + 5x) + -10 = 7 Multiply 6 * 4 24x(7 + 5x) + -10 = 7 (7 * 24x + 5x * 24x) + -10 = 7 (168x + 120x2) + -10 = 7 Reorder the terms: -10 + 168x + 120x2 = 7 Solving -10 + 168x + 120x2 = 7 Solving for variable 'x'. Reorder the terms: -10 + -7 + 168x + 120x2 = 7 + -7 Combine like terms: -10 + -7 = -17 -17 + 168x + 120x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -17 + 168x + 120x2 = 0 Begin completing the square. Divide all terms by 120 the coefficient of the squared term: Divide each side by '120'. -0.1416666667 + 1.4x + x2 = 0.0 Move the constant term to the right: Add '0.1416666667' to each side of the equation. -0.1416666667 + 1.4x + 0.1416666667 + x2 = 0.0 + 0.1416666667 Reorder the terms: -0.1416666667 + 0.1416666667 + 1.4x + x2 = 0.0 + 0.1416666667 Combine like terms: -0.1416666667 + 0.1416666667 = 0.0000000000 0.0000000000 + 1.4x + x2 = 0.0 + 0.1416666667 1.4x + x2 = 0.0 + 0.1416666667 Combine like terms: 0.0 + 0.1416666667 = 0.1416666667 1.4x + x2 = 0.1416666667 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 = 0.1416666667 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 0.1416666667 + 0.49 Combine like terms: 0.1416666667 + 0.49 = 0.6316666667 0.49 + 1.4x + x2 = 0.6316666667 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.6316666667 Calculate the square root of the right side: 0.794774601 Break this problem into two subproblems by setting (x + 0.7) equal to 0.794774601 and -0.794774601.Subproblem 1
x + 0.7 = 0.794774601 Simplifying x + 0.7 = 0.794774601 Reorder the terms: 0.7 + x = 0.794774601 Solving 0.7 + x = 0.794774601 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 = 0.794774601 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.794774601 + -0.7 x = 0.794774601 + -0.7 Combine like terms: 0.794774601 + -0.7 = 0.094774601 x = 0.094774601 Simplifying x = 0.094774601Subproblem 2
x + 0.7 = -0.794774601 Simplifying x + 0.7 = -0.794774601 Reorder the terms: 0.7 + x = -0.794774601 Solving 0.7 + x = -0.794774601 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 = -0.794774601 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.794774601 + -0.7 x = -0.794774601 + -0.7 Combine like terms: -0.794774601 + -0.7 = -1.494774601 x = -1.494774601 Simplifying x = -1.494774601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.094774601, -1.494774601}
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