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Simplifying x2 + -48x + 288 = 0 Reorder the terms: 288 + -48x + x2 = 0 Solving 288 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-288' to each side of the equation. 288 + -48x + -288 + x2 = 0 + -288 Reorder the terms: 288 + -288 + -48x + x2 = 0 + -288 Combine like terms: 288 + -288 = 0 0 + -48x + x2 = 0 + -288 -48x + x2 = 0 + -288 Combine like terms: 0 + -288 = -288 -48x + x2 = -288 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 = -288 + 576 Reorder the terms: 576 + -48x + x2 = -288 + 576 Combine like terms: -288 + 576 = 288 576 + -48x + x2 = 288 Factor a perfect square on the left side: (x + -24)(x + -24) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + -24) equal to 16.970562748 and -16.970562748.Subproblem 1
x + -24 = 16.970562748 Simplifying x + -24 = 16.970562748 Reorder the terms: -24 + x = 16.970562748 Solving -24 + x = 16.970562748 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 = 16.970562748 + 24 Combine like terms: -24 + 24 = 0 0 + x = 16.970562748 + 24 x = 16.970562748 + 24 Combine like terms: 16.970562748 + 24 = 40.970562748 x = 40.970562748 Simplifying x = 40.970562748Subproblem 2
x + -24 = -16.970562748 Simplifying x + -24 = -16.970562748 Reorder the terms: -24 + x = -16.970562748 Solving -24 + x = -16.970562748 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 = -16.970562748 + 24 Combine like terms: -24 + 24 = 0 0 + x = -16.970562748 + 24 x = -16.970562748 + 24 Combine like terms: -16.970562748 + 24 = 7.029437252 x = 7.029437252 Simplifying x = 7.029437252Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.970562748, 7.029437252}
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