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Simplifying (x + -0.5)(3 + -7x) = 0 Reorder the terms: (-0.5 + x)(3 + -7x) = 0 Multiply (-0.5 + x) * (3 + -7x) (-0.5(3 + -7x) + x(3 + -7x)) = 0 ((3 * -0.5 + -7x * -0.5) + x(3 + -7x)) = 0 ((-1.5 + 3.5x) + x(3 + -7x)) = 0 (-1.5 + 3.5x + (3 * x + -7x * x)) = 0 (-1.5 + 3.5x + (3x + -7x2)) = 0 Combine like terms: 3.5x + 3x = 6.5x (-1.5 + 6.5x + -7x2) = 0 Solving -1.5 + 6.5x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.2142857143 + -0.9285714286x + x2 = 0 Move the constant term to the right: Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.9285714286x + -0.2142857143 + x2 = 0 + -0.2142857143 Reorder the terms: 0.2142857143 + -0.2142857143 + -0.9285714286x + x2 = 0 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + -0.9285714286x + x2 = 0 + -0.2142857143 -0.9285714286x + x2 = 0 + -0.2142857143 Combine like terms: 0 + -0.2142857143 = -0.2142857143 -0.9285714286x + x2 = -0.2142857143 The x term is -0.9285714286x. Take half its coefficient (-0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. -0.9285714286x + 0.2155612245 + x2 = -0.2142857143 + 0.2155612245 Reorder the terms: 0.2155612245 + -0.9285714286x + x2 = -0.2142857143 + 0.2155612245 Combine like terms: -0.2142857143 + 0.2155612245 = 0.0012755102 0.2155612245 + -0.9285714286x + x2 = 0.0012755102 Factor a perfect square on the left side: (x + -0.4642857143)(x + -0.4642857143) = 0.0012755102 Calculate the square root of the right side: 0.035714286 Break this problem into two subproblems by setting (x + -0.4642857143) equal to 0.035714286 and -0.035714286.Subproblem 1
x + -0.4642857143 = 0.035714286 Simplifying x + -0.4642857143 = 0.035714286 Reorder the terms: -0.4642857143 + x = 0.035714286 Solving -0.4642857143 + x = 0.035714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = 0.035714286 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = 0.035714286 + 0.4642857143 x = 0.035714286 + 0.4642857143 Combine like terms: 0.035714286 + 0.4642857143 = 0.5000000003 x = 0.5000000003 Simplifying x = 0.5000000003Subproblem 2
x + -0.4642857143 = -0.035714286 Simplifying x + -0.4642857143 = -0.035714286 Reorder the terms: -0.4642857143 + x = -0.035714286 Solving -0.4642857143 + x = -0.035714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = -0.035714286 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = -0.035714286 + 0.4642857143 x = -0.035714286 + 0.4642857143 Combine like terms: -0.035714286 + 0.4642857143 = 0.4285714283 x = 0.4285714283 Simplifying x = 0.4285714283Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5000000003, 0.4285714283}
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