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Simplifying 25 = -1x2 + 24x Reorder the terms: 25 = 24x + -1x2 Solving 25 = 24x + -1x2 Solving for variable 'x'. Reorder the terms: 25 + -24x + x2 = 24x + -24x + -1x2 + x2 Combine like terms: 24x + -24x = 0 25 + -24x + x2 = 0 + -1x2 + x2 25 + -24x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 25 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -24x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -24x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -24x + x2 = 0 + -25 -24x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -24x + x2 = -25 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -25 + 144 Reorder the terms: 144 + -24x + x2 = -25 + 144 Combine like terms: -25 + 144 = 119 144 + -24x + x2 = 119 Factor a perfect square on the left side: (x + -12)(x + -12) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + -12) equal to 10.908712115 and -10.908712115.Subproblem 1
x + -12 = 10.908712115 Simplifying x + -12 = 10.908712115 Reorder the terms: -12 + x = 10.908712115 Solving -12 + x = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.908712115 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.908712115 + 12 x = 10.908712115 + 12 Combine like terms: 10.908712115 + 12 = 22.908712115 x = 22.908712115 Simplifying x = 22.908712115Subproblem 2
x + -12 = -10.908712115 Simplifying x + -12 = -10.908712115 Reorder the terms: -12 + x = -10.908712115 Solving -12 + x = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.908712115 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.908712115 + 12 x = -10.908712115 + 12 Combine like terms: -10.908712115 + 12 = 1.091287885 x = 1.091287885 Simplifying x = 1.091287885Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.908712115, 1.091287885}
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