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Simplifying x2 + 52x + -3 = 0 Reorder the terms: -3 + 52x + x2 = 0 Solving -3 + 52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 52x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 52x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 52x + x2 = 0 + 3 52x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 52x + x2 = 3 The x term is 52x. Take half its coefficient (26). Square it (676) and add it to both sides. Add '676' to each side of the equation. 52x + 676 + x2 = 3 + 676 Reorder the terms: 676 + 52x + x2 = 3 + 676 Combine like terms: 3 + 676 = 679 676 + 52x + x2 = 679 Factor a perfect square on the left side: (x + 26)(x + 26) = 679 Calculate the square root of the right side: 26.057628442 Break this problem into two subproblems by setting (x + 26) equal to 26.057628442 and -26.057628442.Subproblem 1
x + 26 = 26.057628442 Simplifying x + 26 = 26.057628442 Reorder the terms: 26 + x = 26.057628442 Solving 26 + x = 26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = 26.057628442 + -26 Combine like terms: 26 + -26 = 0 0 + x = 26.057628442 + -26 x = 26.057628442 + -26 Combine like terms: 26.057628442 + -26 = 0.057628442 x = 0.057628442 Simplifying x = 0.057628442Subproblem 2
x + 26 = -26.057628442 Simplifying x + 26 = -26.057628442 Reorder the terms: 26 + x = -26.057628442 Solving 26 + x = -26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = -26.057628442 + -26 Combine like terms: 26 + -26 = 0 0 + x = -26.057628442 + -26 x = -26.057628442 + -26 Combine like terms: -26.057628442 + -26 = -52.057628442 x = -52.057628442 Simplifying x = -52.057628442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057628442, -52.057628442}
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