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Simplifying x(x + 7) = 130 Reorder the terms: x(7 + x) = 130 (7 * x + x * x) = 130 (7x + x2) = 130 Solving 7x + x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + 7x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 7x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 7x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 7x + x2 = 0 + 130 7x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 7x + x2 = 130 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 130 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 130 + 12.25 Combine like terms: 130 + 12.25 = 142.25 12.25 + 7x + x2 = 142.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + 3.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + 3.5 = 11.926860442 Simplifying x + 3.5 = 11.926860442 Reorder the terms: 3.5 + x = 11.926860442 Solving 3.5 + x = 11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.926860442 + -3.5 x = 11.926860442 + -3.5 Combine like terms: 11.926860442 + -3.5 = 8.426860442 x = 8.426860442 Simplifying x = 8.426860442Subproblem 2
x + 3.5 = -11.926860442 Simplifying x + 3.5 = -11.926860442 Reorder the terms: 3.5 + x = -11.926860442 Solving 3.5 + x = -11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.926860442 + -3.5 x = -11.926860442 + -3.5 Combine like terms: -11.926860442 + -3.5 = -15.426860442 x = -15.426860442 Simplifying x = -15.426860442Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.426860442, -15.426860442}
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