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Simplifying x(x + -5) = 62 Reorder the terms: x(-5 + x) = 62 (-5 * x + x * x) = 62 (-5x + x2) = 62 Solving -5x + x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + -5x + x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -5x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -5x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -5x + x2 = 0 + 62 -5x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -5x + x2 = 62 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 62 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 62 + 6.25 Combine like terms: 62 + 6.25 = 68.25 6.25 + -5x + x2 = 68.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + -2.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + -2.5 = 8.261355821 Simplifying x + -2.5 = 8.261355821 Reorder the terms: -2.5 + x = 8.261355821 Solving -2.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 8.261355821 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 8.261355821 + 2.5 x = 8.261355821 + 2.5 Combine like terms: 8.261355821 + 2.5 = 10.761355821 x = 10.761355821 Simplifying x = 10.761355821Subproblem 2
x + -2.5 = -8.261355821 Simplifying x + -2.5 = -8.261355821 Reorder the terms: -2.5 + x = -8.261355821 Solving -2.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -8.261355821 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -8.261355821 + 2.5 x = -8.261355821 + 2.5 Combine like terms: -8.261355821 + 2.5 = -5.761355821 x = -5.761355821 Simplifying x = -5.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.761355821, -5.761355821}
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