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Simplifying 7x(x + 1) = 30 Reorder the terms: 7x(1 + x) = 30 (1 * 7x + x * 7x) = 30 (7x + 7x2) = 30 Solving 7x + 7x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 7x + 7x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x + x2 = 0 + 4.285714286 x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 x + x2 = 4.285714286 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 4.285714286 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 4.285714286 + 0.25 Combine like terms: 4.285714286 + 0.25 = 4.535714286 1.25 + x2 = 4.535714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.535714286 Calculate the square root of the right side: 2.129721645 Break this problem into two subproblems by setting (x + 0.5) equal to 2.129721645 and -2.129721645.Subproblem 1
x + 0.5 = 2.129721645 Simplifying x + 0.5 = 2.129721645 Reorder the terms: 0.5 + x = 2.129721645 Solving 0.5 + x = 2.129721645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.129721645 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.129721645 + -0.5 x = 2.129721645 + -0.5 Combine like terms: 2.129721645 + -0.5 = 1.629721645 x = 1.629721645 Simplifying x = 1.629721645Subproblem 2
x + 0.5 = -2.129721645 Simplifying x + 0.5 = -2.129721645 Reorder the terms: 0.5 + x = -2.129721645 Solving 0.5 + x = -2.129721645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.129721645 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.129721645 + -0.5 x = -2.129721645 + -0.5 Combine like terms: -2.129721645 + -0.5 = -2.629721645 x = -2.629721645 Simplifying x = -2.629721645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.629721645, -2.629721645}
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