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Simplifying x2 + -48x + -40 = 0 Reorder the terms: -40 + -48x + x2 = 0 Solving -40 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -48x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -48x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -48x + x2 = 0 + 40 -48x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -48x + x2 = 40 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 40 + 576 Reorder the terms: 576 + -48x + x2 = 40 + 576 Combine like terms: 40 + 576 = 616 576 + -48x + x2 = 616 Factor a perfect square on the left side: (x + -24)(x + -24) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + -24) equal to 24.819347292 and -24.819347292.Subproblem 1
x + -24 = 24.819347292 Simplifying x + -24 = 24.819347292 Reorder the terms: -24 + x = 24.819347292 Solving -24 + x = 24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 24.819347292 + 24 Combine like terms: -24 + 24 = 0 0 + x = 24.819347292 + 24 x = 24.819347292 + 24 Combine like terms: 24.819347292 + 24 = 48.819347292 x = 48.819347292 Simplifying x = 48.819347292Subproblem 2
x + -24 = -24.819347292 Simplifying x + -24 = -24.819347292 Reorder the terms: -24 + x = -24.819347292 Solving -24 + x = -24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -24.819347292 + 24 Combine like terms: -24 + 24 = 0 0 + x = -24.819347292 + 24 x = -24.819347292 + 24 Combine like terms: -24.819347292 + 24 = -0.819347292 x = -0.819347292 Simplifying x = -0.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.819347292, -0.819347292}
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