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Simplifying x2 + -48x + 80 = 0 Reorder the terms: 80 + -48x + x2 = 0 Solving 80 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -48x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -48x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -48x + x2 = 0 + -80 -48x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -48x + x2 = -80 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 = -80 + 576 Reorder the terms: 576 + -48x + x2 = -80 + 576 Combine like terms: -80 + 576 = 496 576 + -48x + x2 = 496 Factor a perfect square on the left side: (x + -24)(x + -24) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + -24) equal to 22.271057451 and -22.271057451.Subproblem 1
x + -24 = 22.271057451 Simplifying x + -24 = 22.271057451 Reorder the terms: -24 + x = 22.271057451 Solving -24 + x = 22.271057451 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 = 22.271057451 + 24 Combine like terms: -24 + 24 = 0 0 + x = 22.271057451 + 24 x = 22.271057451 + 24 Combine like terms: 22.271057451 + 24 = 46.271057451 x = 46.271057451 Simplifying x = 46.271057451Subproblem 2
x + -24 = -22.271057451 Simplifying x + -24 = -22.271057451 Reorder the terms: -24 + x = -22.271057451 Solving -24 + x = -22.271057451 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 = -22.271057451 + 24 Combine like terms: -24 + 24 = 0 0 + x = -22.271057451 + 24 x = -22.271057451 + 24 Combine like terms: -22.271057451 + 24 = 1.728942549 x = 1.728942549 Simplifying x = 1.728942549Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.271057451, 1.728942549}
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