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Simplifying x2 + -58x + 144 = 0 Reorder the terms: 144 + -58x + x2 = 0 Solving 144 + -58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -58x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -58x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -58x + x2 = 0 + -144 -58x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -58x + x2 = -144 The x term is -58x. Take half its coefficient (-29). Square it (841) and add it to both sides. Add '841' to each side of the equation. -58x + 841 + x2 = -144 + 841 Reorder the terms: 841 + -58x + x2 = -144 + 841 Combine like terms: -144 + 841 = 697 841 + -58x + x2 = 697 Factor a perfect square on the left side: (x + -29)(x + -29) = 697 Calculate the square root of the right side: 26.400757565 Break this problem into two subproblems by setting (x + -29) equal to 26.400757565 and -26.400757565.Subproblem 1
x + -29 = 26.400757565 Simplifying x + -29 = 26.400757565 Reorder the terms: -29 + x = 26.400757565 Solving -29 + x = 26.400757565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + x = 26.400757565 + 29 Combine like terms: -29 + 29 = 0 0 + x = 26.400757565 + 29 x = 26.400757565 + 29 Combine like terms: 26.400757565 + 29 = 55.400757565 x = 55.400757565 Simplifying x = 55.400757565Subproblem 2
x + -29 = -26.400757565 Simplifying x + -29 = -26.400757565 Reorder the terms: -29 + x = -26.400757565 Solving -29 + x = -26.400757565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + x = -26.400757565 + 29 Combine like terms: -29 + 29 = 0 0 + x = -26.400757565 + 29 x = -26.400757565 + 29 Combine like terms: -26.400757565 + 29 = 2.599242435 x = 2.599242435 Simplifying x = 2.599242435Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.400757565, 2.599242435}
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