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Simplifying x2 + -10x + 25 = 200 Reorder the terms: 25 + -10x + x2 = 200 Solving 25 + -10x + x2 = 200 Solving for variable 'x'. Reorder the terms: 25 + -200 + -10x + x2 = 200 + -200 Combine like terms: 25 + -200 = -175 -175 + -10x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -175 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + -10x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + -10x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -10x + x2 = 0 + 175 -10x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 -10x + x2 = 175 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 = 175 + 25 Reorder the terms: 25 + -10x + x2 = 175 + 25 Combine like terms: 175 + 25 = 200 25 + -10x + x2 = 200 Factor a perfect square on the left side: (x + -5)(x + -5) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -5) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -5 = 14.142135624 Simplifying x + -5 = 14.142135624 Reorder the terms: -5 + x = 14.142135624 Solving -5 + x = 14.142135624 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 = 14.142135624 + 5 Combine like terms: -5 + 5 = 0 0 + x = 14.142135624 + 5 x = 14.142135624 + 5 Combine like terms: 14.142135624 + 5 = 19.142135624 x = 19.142135624 Simplifying x = 19.142135624Subproblem 2
x + -5 = -14.142135624 Simplifying x + -5 = -14.142135624 Reorder the terms: -5 + x = -14.142135624 Solving -5 + x = -14.142135624 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 = -14.142135624 + 5 Combine like terms: -5 + 5 = 0 0 + x = -14.142135624 + 5 x = -14.142135624 + 5 Combine like terms: -14.142135624 + 5 = -9.142135624 x = -9.142135624 Simplifying x = -9.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.142135624, -9.142135624}
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