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Simplifying 0 = 2x2 + 10x + -1016 Reorder the terms: 0 = -1016 + 10x + 2x2 Solving 0 = -1016 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 1016 = 1016 1016 + -10x + -2x2 = -1016 + 10x + 2x2 + 1016 + -10x + -2x2 Reorder the terms: 1016 + -10x + -2x2 = -1016 + 1016 + 10x + -10x + 2x2 + -2x2 Combine like terms: -1016 + 1016 = 0 1016 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 1016 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 1016 + -10x + -2x2 = 0 + 2x2 + -2x2 1016 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1016 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(508 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(508 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 508 + -5x + -1x2 = 0 Solving 508 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -508 + 5x + x2 = 0 Move the constant term to the right: Add '508' to each side of the equation. -508 + 5x + 508 + x2 = 0 + 508 Reorder the terms: -508 + 508 + 5x + x2 = 0 + 508 Combine like terms: -508 + 508 = 0 0 + 5x + x2 = 0 + 508 5x + x2 = 0 + 508 Combine like terms: 0 + 508 = 508 5x + x2 = 508 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 = 508 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 508 + 6.25 Combine like terms: 508 + 6.25 = 514.25 6.25 + 5x + x2 = 514.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 514.25 Calculate the square root of the right side: 22.677080941 Break this problem into two subproblems by setting (x + 2.5) equal to 22.677080941 and -22.677080941.Subproblem 1
x + 2.5 = 22.677080941 Simplifying x + 2.5 = 22.677080941 Reorder the terms: 2.5 + x = 22.677080941 Solving 2.5 + x = 22.677080941 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 = 22.677080941 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 22.677080941 + -2.5 x = 22.677080941 + -2.5 Combine like terms: 22.677080941 + -2.5 = 20.177080941 x = 20.177080941 Simplifying x = 20.177080941Subproblem 2
x + 2.5 = -22.677080941 Simplifying x + 2.5 = -22.677080941 Reorder the terms: 2.5 + x = -22.677080941 Solving 2.5 + x = -22.677080941 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 = -22.677080941 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -22.677080941 + -2.5 x = -22.677080941 + -2.5 Combine like terms: -22.677080941 + -2.5 = -25.177080941 x = -25.177080941 Simplifying x = -25.177080941Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.177080941, -25.177080941}Solution
x = {20.177080941, -25.177080941}
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