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Simplifying 7x + (x + -20) * x = 180 Reorder the terms: 7x + (-20 + x) * x = 180 Reorder the terms for easier multiplication: 7x + x(-20 + x) = 180 7x + (-20 * x + x * x) = 180 7x + (-20x + x2) = 180 Combine like terms: 7x + -20x = -13x -13x + x2 = 180 Solving -13x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -13x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -13x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -13x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -13x + x2 = 0 + 180 -13x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -13x + x2 = 180 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 180 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 180 + 42.25 Combine like terms: 180 + 42.25 = 222.25 42.25 + -13x + x2 = 222.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + -6.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + -6.5 = 14.908051516 Simplifying x + -6.5 = 14.908051516 Reorder the terms: -6.5 + x = 14.908051516 Solving -6.5 + x = 14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 14.908051516 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 14.908051516 + 6.5 x = 14.908051516 + 6.5 Combine like terms: 14.908051516 + 6.5 = 21.408051516 x = 21.408051516 Simplifying x = 21.408051516Subproblem 2
x + -6.5 = -14.908051516 Simplifying x + -6.5 = -14.908051516 Reorder the terms: -6.5 + x = -14.908051516 Solving -6.5 + x = -14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -14.908051516 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -14.908051516 + 6.5 x = -14.908051516 + 6.5 Combine like terms: -14.908051516 + 6.5 = -8.408051516 x = -8.408051516 Simplifying x = -8.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.408051516, -8.408051516}
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