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Simplifying x2 + -47x + 15 = 0 Reorder the terms: 15 + -47x + x2 = 0 Solving 15 + -47x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -47x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -47x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -47x + x2 = 0 + -15 -47x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -47x + x2 = -15 The x term is -47x. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47x + 552.25 + x2 = -15 + 552.25 Reorder the terms: 552.25 + -47x + x2 = -15 + 552.25 Combine like terms: -15 + 552.25 = 537.25 552.25 + -47x + x2 = 537.25 Factor a perfect square on the left side: (x + -23.5)(x + -23.5) = 537.25 Calculate the square root of the right side: 23.178653973 Break this problem into two subproblems by setting (x + -23.5) equal to 23.178653973 and -23.178653973.Subproblem 1
x + -23.5 = 23.178653973 Simplifying x + -23.5 = 23.178653973 Reorder the terms: -23.5 + x = 23.178653973 Solving -23.5 + x = 23.178653973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = 23.178653973 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = 23.178653973 + 23.5 x = 23.178653973 + 23.5 Combine like terms: 23.178653973 + 23.5 = 46.678653973 x = 46.678653973 Simplifying x = 46.678653973Subproblem 2
x + -23.5 = -23.178653973 Simplifying x + -23.5 = -23.178653973 Reorder the terms: -23.5 + x = -23.178653973 Solving -23.5 + x = -23.178653973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = -23.178653973 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = -23.178653973 + 23.5 x = -23.178653973 + 23.5 Combine like terms: -23.178653973 + 23.5 = 0.321346027 x = 0.321346027 Simplifying x = 0.321346027Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.678653973, 0.321346027}
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