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Simplifying x2 + -62x + 48 = 0 Reorder the terms: 48 + -62x + x2 = 0 Solving 48 + -62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -62x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -62x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -62x + x2 = 0 + -48 -62x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -62x + x2 = -48 The x term is -62x. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62x + 961 + x2 = -48 + 961 Reorder the terms: 961 + -62x + x2 = -48 + 961 Combine like terms: -48 + 961 = 913 961 + -62x + x2 = 913 Factor a perfect square on the left side: (x + -31)(x + -31) = 913 Calculate the square root of the right side: 30.215889859 Break this problem into two subproblems by setting (x + -31) equal to 30.215889859 and -30.215889859.Subproblem 1
x + -31 = 30.215889859 Simplifying x + -31 = 30.215889859 Reorder the terms: -31 + x = 30.215889859 Solving -31 + x = 30.215889859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 30.215889859 + 31 Combine like terms: -31 + 31 = 0 0 + x = 30.215889859 + 31 x = 30.215889859 + 31 Combine like terms: 30.215889859 + 31 = 61.215889859 x = 61.215889859 Simplifying x = 61.215889859Subproblem 2
x + -31 = -30.215889859 Simplifying x + -31 = -30.215889859 Reorder the terms: -31 + x = -30.215889859 Solving -31 + x = -30.215889859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = -30.215889859 + 31 Combine like terms: -31 + 31 = 0 0 + x = -30.215889859 + 31 x = -30.215889859 + 31 Combine like terms: -30.215889859 + 31 = 0.784110141 x = 0.784110141 Simplifying x = 0.784110141Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.215889859, 0.784110141}
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