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Simplifying x2 + 46x + -87 = 0 Reorder the terms: -87 + 46x + x2 = 0 Solving -87 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 46x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 46x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 46x + x2 = 0 + 87 46x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 46x + x2 = 87 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 87 + 529 Reorder the terms: 529 + 46x + x2 = 87 + 529 Combine like terms: 87 + 529 = 616 529 + 46x + x2 = 616 Factor a perfect square on the left side: (x + 23)(x + 23) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + 23) equal to 24.819347292 and -24.819347292.Subproblem 1
x + 23 = 24.819347292 Simplifying x + 23 = 24.819347292 Reorder the terms: 23 + x = 24.819347292 Solving 23 + x = 24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 24.819347292 + -23 Combine like terms: 23 + -23 = 0 0 + x = 24.819347292 + -23 x = 24.819347292 + -23 Combine like terms: 24.819347292 + -23 = 1.819347292 x = 1.819347292 Simplifying x = 1.819347292Subproblem 2
x + 23 = -24.819347292 Simplifying x + 23 = -24.819347292 Reorder the terms: 23 + x = -24.819347292 Solving 23 + x = -24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -24.819347292 + -23 Combine like terms: 23 + -23 = 0 0 + x = -24.819347292 + -23 x = -24.819347292 + -23 Combine like terms: -24.819347292 + -23 = -47.819347292 x = -47.819347292 Simplifying x = -47.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.819347292, -47.819347292}
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