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Simplifying 260 = 4x2 + 22x Reorder the terms: 260 = 22x + 4x2 Solving 260 = 22x + 4x2 Solving for variable 'x'. Reorder the terms: 260 + -22x + -4x2 = 22x + -22x + 4x2 + -4x2 Combine like terms: 22x + -22x = 0 260 + -22x + -4x2 = 0 + 4x2 + -4x2 260 + -22x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 260 + -22x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(130 + -11x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(130 + -11x + -2x2)' equal to zero and attempt to solve: Simplifying 130 + -11x + -2x2 = 0 Solving 130 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -65 + 5.5x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + 5.5x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 5.5x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 5.5x + x2 = 0 + 65 5.5x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 5.5x + x2 = 65 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 65 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 65 + 7.5625 Combine like terms: 65 + 7.5625 = 72.5625 7.5625 + 5.5x + x2 = 72.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (x + 2.75) equal to 8.518362519 and -8.518362519.Subproblem 1
x + 2.75 = 8.518362519 Simplifying x + 2.75 = 8.518362519 Reorder the terms: 2.75 + x = 8.518362519 Solving 2.75 + x = 8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 8.518362519 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 8.518362519 + -2.75 x = 8.518362519 + -2.75 Combine like terms: 8.518362519 + -2.75 = 5.768362519 x = 5.768362519 Simplifying x = 5.768362519Subproblem 2
x + 2.75 = -8.518362519 Simplifying x + 2.75 = -8.518362519 Reorder the terms: 2.75 + x = -8.518362519 Solving 2.75 + x = -8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -8.518362519 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -8.518362519 + -2.75 x = -8.518362519 + -2.75 Combine like terms: -8.518362519 + -2.75 = -11.268362519 x = -11.268362519 Simplifying x = -11.268362519Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.768362519, -11.268362519}Solution
x = {5.768362519, -11.268362519}
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