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Simplifying x2 + 4x + -7500 = 0 Reorder the terms: -7500 + 4x + x2 = 0 Solving -7500 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7500' to each side of the equation. -7500 + 4x + 7500 + x2 = 0 + 7500 Reorder the terms: -7500 + 7500 + 4x + x2 = 0 + 7500 Combine like terms: -7500 + 7500 = 0 0 + 4x + x2 = 0 + 7500 4x + x2 = 0 + 7500 Combine like terms: 0 + 7500 = 7500 4x + x2 = 7500 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7500 + 4 Reorder the terms: 4 + 4x + x2 = 7500 + 4 Combine like terms: 7500 + 4 = 7504 4 + 4x + x2 = 7504 Factor a perfect square on the left side: (x + 2)(x + 2) = 7504 Calculate the square root of the right side: 86.625631311 Break this problem into two subproblems by setting (x + 2) equal to 86.625631311 and -86.625631311.Subproblem 1
x + 2 = 86.625631311 Simplifying x + 2 = 86.625631311 Reorder the terms: 2 + x = 86.625631311 Solving 2 + x = 86.625631311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 86.625631311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 86.625631311 + -2 x = 86.625631311 + -2 Combine like terms: 86.625631311 + -2 = 84.625631311 x = 84.625631311 Simplifying x = 84.625631311Subproblem 2
x + 2 = -86.625631311 Simplifying x + 2 = -86.625631311 Reorder the terms: 2 + x = -86.625631311 Solving 2 + x = -86.625631311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -86.625631311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -86.625631311 + -2 x = -86.625631311 + -2 Combine like terms: -86.625631311 + -2 = -88.625631311 x = -88.625631311 Simplifying x = -88.625631311Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.625631311, -88.625631311}
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