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Simplifying 10x + 200 = x2 + 5x Reorder the terms: 200 + 10x = x2 + 5x Reorder the terms: 200 + 10x = 5x + x2 Solving 200 + 10x = 5x + x2 Solving for variable 'x'. Combine like terms: 10x + -5x = 5x 200 + 5x + -1x2 = 5x + x2 + -5x + -1x2 Reorder the terms: 200 + 5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 200 + 5x + -1x2 = 0 + x2 + -1x2 200 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 200 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + -5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -5x + x2 = 0 + 200 -5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -5x + x2 = 200 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 = 200 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 200 + 6.25 Combine like terms: 200 + 6.25 = 206.25 6.25 + -5x + x2 = 206.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (x + -2.5) equal to 14.361406616 and -14.361406616.Subproblem 1
x + -2.5 = 14.361406616 Simplifying x + -2.5 = 14.361406616 Reorder the terms: -2.5 + x = 14.361406616 Solving -2.5 + x = 14.361406616 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 = 14.361406616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 14.361406616 + 2.5 x = 14.361406616 + 2.5 Combine like terms: 14.361406616 + 2.5 = 16.861406616 x = 16.861406616 Simplifying x = 16.861406616Subproblem 2
x + -2.5 = -14.361406616 Simplifying x + -2.5 = -14.361406616 Reorder the terms: -2.5 + x = -14.361406616 Solving -2.5 + x = -14.361406616 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 = -14.361406616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -14.361406616 + 2.5 x = -14.361406616 + 2.5 Combine like terms: -14.361406616 + 2.5 = -11.861406616 x = -11.861406616 Simplifying x = -11.861406616Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.861406616, -11.861406616}
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