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Simplifying x2 + -35x + 24 = 0 Reorder the terms: 24 + -35x + x2 = 0 Solving 24 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -35x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -35x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -35x + x2 = 0 + -24 -35x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -35x + x2 = -24 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -24 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -24 + 306.25 Combine like terms: -24 + 306.25 = 282.25 306.25 + -35x + x2 = 282.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (x + -17.5) equal to 16.800297616 and -16.800297616.Subproblem 1
x + -17.5 = 16.800297616 Simplifying x + -17.5 = 16.800297616 Reorder the terms: -17.5 + x = 16.800297616 Solving -17.5 + x = 16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 16.800297616 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 16.800297616 + 17.5 x = 16.800297616 + 17.5 Combine like terms: 16.800297616 + 17.5 = 34.300297616 x = 34.300297616 Simplifying x = 34.300297616Subproblem 2
x + -17.5 = -16.800297616 Simplifying x + -17.5 = -16.800297616 Reorder the terms: -17.5 + x = -16.800297616 Solving -17.5 + x = -16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -16.800297616 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -16.800297616 + 17.5 x = -16.800297616 + 17.5 Combine like terms: -16.800297616 + 17.5 = 0.699702384 x = 0.699702384 Simplifying x = 0.699702384Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.300297616, 0.699702384}
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