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Simplifying x = (7x + 1)(x + -3) Reorder the terms: x = (1 + 7x)(x + -3) Reorder the terms: x = (1 + 7x)(-3 + x) Multiply (1 + 7x) * (-3 + x) x = (1(-3 + x) + 7x * (-3 + x)) x = ((-3 * 1 + x * 1) + 7x * (-3 + x)) x = ((-3 + 1x) + 7x * (-3 + x)) x = (-3 + 1x + (-3 * 7x + x * 7x)) x = (-3 + 1x + (-21x + 7x2)) Combine like terms: 1x + -21x = -20x x = (-3 + -20x + 7x2) Solving x = -3 + -20x + 7x2 Solving for variable 'x'. Reorder the terms: 3 + x + 20x + -7x2 = -3 + -20x + 7x2 + 3 + 20x + -7x2 Combine like terms: x + 20x = 21x 3 + 21x + -7x2 = -3 + -20x + 7x2 + 3 + 20x + -7x2 Reorder the terms: 3 + 21x + -7x2 = -3 + 3 + -20x + 20x + 7x2 + -7x2 Combine like terms: -3 + 3 = 0 3 + 21x + -7x2 = 0 + -20x + 20x + 7x2 + -7x2 3 + 21x + -7x2 = -20x + 20x + 7x2 + -7x2 Combine like terms: -20x + 20x = 0 3 + 21x + -7x2 = 0 + 7x2 + -7x2 3 + 21x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 3 + 21x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.4285714286 + -3x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -3x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -3x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.4285714286 -3x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -3x + x2 = 0.4285714286 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.4285714286 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.4285714286 + 2.25 Combine like terms: 0.4285714286 + 2.25 = 2.6785714286 2.25 + -3x + x2 = 2.6785714286 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.6785714286 Calculate the square root of the right side: 1.636634177 Break this problem into two subproblems by setting (x + -1.5) equal to 1.636634177 and -1.636634177.Subproblem 1
x + -1.5 = 1.636634177 Simplifying x + -1.5 = 1.636634177 Reorder the terms: -1.5 + x = 1.636634177 Solving -1.5 + x = 1.636634177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.636634177 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.636634177 + 1.5 x = 1.636634177 + 1.5 Combine like terms: 1.636634177 + 1.5 = 3.136634177 x = 3.136634177 Simplifying x = 3.136634177Subproblem 2
x + -1.5 = -1.636634177 Simplifying x + -1.5 = -1.636634177 Reorder the terms: -1.5 + x = -1.636634177 Solving -1.5 + x = -1.636634177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.636634177 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.636634177 + 1.5 x = -1.636634177 + 1.5 Combine like terms: -1.636634177 + 1.5 = -0.136634177 x = -0.136634177 Simplifying x = -0.136634177Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.136634177, -0.136634177}
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