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Simplifying 0 = x2 + 58x + -49 Reorder the terms: 0 = -49 + 58x + x2 Solving 0 = -49 + 58x + x2 Solving for variable 'x'. Combine like terms: 0 + 49 = 49 49 + -58x + -1x2 = -49 + 58x + x2 + 49 + -58x + -1x2 Reorder the terms: 49 + -58x + -1x2 = -49 + 49 + 58x + -58x + x2 + -1x2 Combine like terms: -49 + 49 = 0 49 + -58x + -1x2 = 0 + 58x + -58x + x2 + -1x2 49 + -58x + -1x2 = 58x + -58x + x2 + -1x2 Combine like terms: 58x + -58x = 0 49 + -58x + -1x2 = 0 + x2 + -1x2 49 + -58x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 49 + -58x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 58x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 58x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 58x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 58x + x2 = 0 + 49 58x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 58x + x2 = 49 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 = 49 + 841 Reorder the terms: 841 + 58x + x2 = 49 + 841 Combine like terms: 49 + 841 = 890 841 + 58x + x2 = 890 Factor a perfect square on the left side: (x + 29)(x + 29) = 890 Calculate the square root of the right side: 29.83286778 Break this problem into two subproblems by setting (x + 29) equal to 29.83286778 and -29.83286778.Subproblem 1
x + 29 = 29.83286778 Simplifying x + 29 = 29.83286778 Reorder the terms: 29 + x = 29.83286778 Solving 29 + x = 29.83286778 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 = 29.83286778 + -29 Combine like terms: 29 + -29 = 0 0 + x = 29.83286778 + -29 x = 29.83286778 + -29 Combine like terms: 29.83286778 + -29 = 0.83286778 x = 0.83286778 Simplifying x = 0.83286778Subproblem 2
x + 29 = -29.83286778 Simplifying x + 29 = -29.83286778 Reorder the terms: 29 + x = -29.83286778 Solving 29 + x = -29.83286778 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 = -29.83286778 + -29 Combine like terms: 29 + -29 = 0 0 + x = -29.83286778 + -29 x = -29.83286778 + -29 Combine like terms: -29.83286778 + -29 = -58.83286778 x = -58.83286778 Simplifying x = -58.83286778Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.83286778, -58.83286778}
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