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Simplifying x(7x + -4) = 1 Reorder the terms: x(-4 + 7x) = 1 (-4 * x + 7x * x) = 1 (-4x + 7x2) = 1 Solving -4x + 7x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -4x + 7x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.5714285714x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.5714285714x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.1428571429 -0.5714285714x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.5714285714x + x2 = 0.1428571429 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.1428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.1428571429 + 0.08163265305 Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595 0.08163265305 + -0.5714285714x + x2 = 0.22448979595 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.22448979595 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.473803542 and -0.473803542.Subproblem 1
x + -0.2857142857 = 0.473803542 Simplifying x + -0.2857142857 = 0.473803542 Reorder the terms: -0.2857142857 + x = 0.473803542 Solving -0.2857142857 + x = 0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.473803542 + 0.2857142857 x = 0.473803542 + 0.2857142857 Combine like terms: 0.473803542 + 0.2857142857 = 0.7595178277 x = 0.7595178277 Simplifying x = 0.7595178277Subproblem 2
x + -0.2857142857 = -0.473803542 Simplifying x + -0.2857142857 = -0.473803542 Reorder the terms: -0.2857142857 + x = -0.473803542 Solving -0.2857142857 + x = -0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.473803542 + 0.2857142857 x = -0.473803542 + 0.2857142857 Combine like terms: -0.473803542 + 0.2857142857 = -0.1880892563 x = -0.1880892563 Simplifying x = -0.1880892563Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7595178277, -0.1880892563}
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