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Simplifying -2x2 + 10x + 25 = 0 Reorder the terms: 25 + 10x + -2x2 = 0 Solving 25 + 10x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -5x + x2 = 0 + 12.5 -5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -5x + x2 = 12.5 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 = 12.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 12.5 + 6.25 Combine like terms: 12.5 + 6.25 = 18.75 6.25 + -5x + x2 = 18.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -2.5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -2.5 = 4.330127019 Simplifying x + -2.5 = 4.330127019 Reorder the terms: -2.5 + x = 4.330127019 Solving -2.5 + x = 4.330127019 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 = 4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.330127019 + 2.5 x = 4.330127019 + 2.5 Combine like terms: 4.330127019 + 2.5 = 6.830127019 x = 6.830127019 Simplifying x = 6.830127019Subproblem 2
x + -2.5 = -4.330127019 Simplifying x + -2.5 = -4.330127019 Reorder the terms: -2.5 + x = -4.330127019 Solving -2.5 + x = -4.330127019 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 = -4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.330127019 + 2.5 x = -4.330127019 + 2.5 Combine like terms: -4.330127019 + 2.5 = -1.830127019 x = -1.830127019 Simplifying x = -1.830127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.830127019, -1.830127019}
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