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Simplifying x2 + -6x + 9 + 24x + -625 = 0 Reorder the terms: 9 + -625 + -6x + 24x + x2 = 0 Combine like terms: 9 + -625 = -616 -616 + -6x + 24x + x2 = 0 Combine like terms: -6x + 24x = 18x -616 + 18x + x2 = 0 Solving -616 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '616' to each side of the equation. -616 + 18x + 616 + x2 = 0 + 616 Reorder the terms: -616 + 616 + 18x + x2 = 0 + 616 Combine like terms: -616 + 616 = 0 0 + 18x + x2 = 0 + 616 18x + x2 = 0 + 616 Combine like terms: 0 + 616 = 616 18x + x2 = 616 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 616 + 81 Reorder the terms: 81 + 18x + x2 = 616 + 81 Combine like terms: 616 + 81 = 697 81 + 18x + x2 = 697 Factor a perfect square on the left side: (x + 9)(x + 9) = 697 Calculate the square root of the right side: 26.400757565 Break this problem into two subproblems by setting (x + 9) equal to 26.400757565 and -26.400757565.Subproblem 1
x + 9 = 26.400757565 Simplifying x + 9 = 26.400757565 Reorder the terms: 9 + x = 26.400757565 Solving 9 + x = 26.400757565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 26.400757565 + -9 Combine like terms: 9 + -9 = 0 0 + x = 26.400757565 + -9 x = 26.400757565 + -9 Combine like terms: 26.400757565 + -9 = 17.400757565 x = 17.400757565 Simplifying x = 17.400757565Subproblem 2
x + 9 = -26.400757565 Simplifying x + 9 = -26.400757565 Reorder the terms: 9 + x = -26.400757565 Solving 9 + x = -26.400757565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -26.400757565 + -9 Combine like terms: 9 + -9 = 0 0 + x = -26.400757565 + -9 x = -26.400757565 + -9 Combine like terms: -26.400757565 + -9 = -35.400757565 x = -35.400757565 Simplifying x = -35.400757565Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.400757565, -35.400757565}
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