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Simplifying x(x + -2) = 7200 Reorder the terms: x(-2 + x) = 7200 (-2 * x + x * x) = 7200 (-2x + x2) = 7200 Solving -2x + x2 = 7200 Solving for variable 'x'. Reorder the terms: -7200 + -2x + x2 = 7200 + -7200 Combine like terms: 7200 + -7200 = 0 -7200 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7200' to each side of the equation. -7200 + -2x + 7200 + x2 = 0 + 7200 Reorder the terms: -7200 + 7200 + -2x + x2 = 0 + 7200 Combine like terms: -7200 + 7200 = 0 0 + -2x + x2 = 0 + 7200 -2x + x2 = 0 + 7200 Combine like terms: 0 + 7200 = 7200 -2x + x2 = 7200 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 7200 + 1 Reorder the terms: 1 + -2x + x2 = 7200 + 1 Combine like terms: 7200 + 1 = 7201 1 + -2x + x2 = 7201 Factor a perfect square on the left side: (x + -1)(x + -1) = 7201 Calculate the square root of the right side: 84.858706094 Break this problem into two subproblems by setting (x + -1) equal to 84.858706094 and -84.858706094.Subproblem 1
x + -1 = 84.858706094 Simplifying x + -1 = 84.858706094 Reorder the terms: -1 + x = 84.858706094 Solving -1 + x = 84.858706094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 84.858706094 + 1 Combine like terms: -1 + 1 = 0 0 + x = 84.858706094 + 1 x = 84.858706094 + 1 Combine like terms: 84.858706094 + 1 = 85.858706094 x = 85.858706094 Simplifying x = 85.858706094Subproblem 2
x + -1 = -84.858706094 Simplifying x + -1 = -84.858706094 Reorder the terms: -1 + x = -84.858706094 Solving -1 + x = -84.858706094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -84.858706094 + 1 Combine like terms: -1 + 1 = 0 0 + x = -84.858706094 + 1 x = -84.858706094 + 1 Combine like terms: -84.858706094 + 1 = -83.858706094 x = -83.858706094 Simplifying x = -83.858706094Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.858706094, -83.858706094}
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