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Simplifying x2 + -40x = 9.6 Reorder the terms: -40x + x2 = 9.6 Solving -40x + x2 = 9.6 Solving for variable 'x'. Reorder the terms: -9.6 + -40x + x2 = 9.6 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 -9.6 + -40x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -40x + 9.6 + x2 = 0.0 + 9.6 Reorder the terms: -9.6 + 9.6 + -40x + x2 = 0.0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -40x + x2 = 0.0 + 9.6 -40x + x2 = 0.0 + 9.6 Combine like terms: 0.0 + 9.6 = 9.6 -40x + x2 = 9.6 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 9.6 + 400 Reorder the terms: 400 + -40x + x2 = 9.6 + 400 Combine like terms: 9.6 + 400 = 409.6 400 + -40x + x2 = 409.6 Factor a perfect square on the left side: (x + -20)(x + -20) = 409.6 Calculate the square root of the right side: 20.238577025 Break this problem into two subproblems by setting (x + -20) equal to 20.238577025 and -20.238577025.Subproblem 1
x + -20 = 20.238577025 Simplifying x + -20 = 20.238577025 Reorder the terms: -20 + x = 20.238577025 Solving -20 + x = 20.238577025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.238577025 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.238577025 + 20 x = 20.238577025 + 20 Combine like terms: 20.238577025 + 20 = 40.238577025 x = 40.238577025 Simplifying x = 40.238577025Subproblem 2
x + -20 = -20.238577025 Simplifying x + -20 = -20.238577025 Reorder the terms: -20 + x = -20.238577025 Solving -20 + x = -20.238577025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.238577025 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.238577025 + 20 x = -20.238577025 + 20 Combine like terms: -20.238577025 + 20 = -0.238577025 x = -0.238577025 Simplifying x = -0.238577025Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.238577025, -0.238577025}
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