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Simplifying x2 + -5 * 4x = 180 Multiply -5 * 4 x2 + -20x = 180 Reorder the terms: -20x + x2 = 180 Solving -20x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -20x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -20x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -20x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -20x + x2 = 0 + 180 -20x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -20x + x2 = 180 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 180 + 100 Reorder the terms: 100 + -20x + x2 = 180 + 100 Combine like terms: 180 + 100 = 280 100 + -20x + x2 = 280 Factor a perfect square on the left side: (x + -10)(x + -10) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + -10) equal to 16.733200531 and -16.733200531.Subproblem 1
x + -10 = 16.733200531 Simplifying x + -10 = 16.733200531 Reorder the terms: -10 + x = 16.733200531 Solving -10 + x = 16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 16.733200531 + 10 Combine like terms: -10 + 10 = 0 0 + x = 16.733200531 + 10 x = 16.733200531 + 10 Combine like terms: 16.733200531 + 10 = 26.733200531 x = 26.733200531 Simplifying x = 26.733200531Subproblem 2
x + -10 = -16.733200531 Simplifying x + -10 = -16.733200531 Reorder the terms: -10 + x = -16.733200531 Solving -10 + x = -16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -16.733200531 + 10 Combine like terms: -10 + 10 = 0 0 + x = -16.733200531 + 10 x = -16.733200531 + 10 Combine like terms: -16.733200531 + 10 = -6.733200531 x = -6.733200531 Simplifying x = -6.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.733200531, -6.733200531}
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