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Simplifying x2 + -20x = -7 Reorder the terms: -20x + x2 = -7 Solving -20x + x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + -20x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -20x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -20x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -20x + x2 = 0 + -7 -20x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -20x + x2 = -7 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 = -7 + 100 Reorder the terms: 100 + -20x + x2 = -7 + 100 Combine like terms: -7 + 100 = 93 100 + -20x + x2 = 93 Factor a perfect square on the left side: (x + -10)(x + -10) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (x + -10) equal to 9.643650761 and -9.643650761.Subproblem 1
x + -10 = 9.643650761 Simplifying x + -10 = 9.643650761 Reorder the terms: -10 + x = 9.643650761 Solving -10 + x = 9.643650761 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 = 9.643650761 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.643650761 + 10 x = 9.643650761 + 10 Combine like terms: 9.643650761 + 10 = 19.643650761 x = 19.643650761 Simplifying x = 19.643650761Subproblem 2
x + -10 = -9.643650761 Simplifying x + -10 = -9.643650761 Reorder the terms: -10 + x = -9.643650761 Solving -10 + x = -9.643650761 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 = -9.643650761 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.643650761 + 10 x = -9.643650761 + 10 Combine like terms: -9.643650761 + 10 = 0.356349239 x = 0.356349239 Simplifying x = 0.356349239Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.643650761, 0.356349239}
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