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Simplifying x2 + 10x + -224 = 0 Reorder the terms: -224 + 10x + x2 = 0 Solving -224 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 10x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 10x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 10x + x2 = 0 + 224 10x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 10x + x2 = 224 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 224 + 25 Reorder the terms: 25 + 10x + x2 = 224 + 25 Combine like terms: 224 + 25 = 249 25 + 10x + x2 = 249 Factor a perfect square on the left side: (x + 5)(x + 5) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (x + 5) equal to 15.779733838 and -15.779733838.Subproblem 1
x + 5 = 15.779733838 Simplifying x + 5 = 15.779733838 Reorder the terms: 5 + x = 15.779733838 Solving 5 + x = 15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 15.779733838 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.779733838 + -5 x = 15.779733838 + -5 Combine like terms: 15.779733838 + -5 = 10.779733838 x = 10.779733838 Simplifying x = 10.779733838Subproblem 2
x + 5 = -15.779733838 Simplifying x + 5 = -15.779733838 Reorder the terms: 5 + x = -15.779733838 Solving 5 + x = -15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -15.779733838 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.779733838 + -5 x = -15.779733838 + -5 Combine like terms: -15.779733838 + -5 = -20.779733838 x = -20.779733838 Simplifying x = -20.779733838Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.779733838, -20.779733838}
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