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Simplifying 2x2 + 14x = 220 Reorder the terms: 14x + 2x2 = 220 Solving 14x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + 14x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-110 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-110 + 7x + x2)' equal to zero and attempt to solve: Simplifying -110 + 7x + x2 = 0 Solving -110 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 7x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 7x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 7x + x2 = 0 + 110 7x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 7x + x2 = 110 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 110 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 110 + 12.25 Combine like terms: 110 + 12.25 = 122.25 12.25 + 7x + x2 = 122.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + 3.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + 3.5 = 11.056672194 Simplifying x + 3.5 = 11.056672194 Reorder the terms: 3.5 + x = 11.056672194 Solving 3.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.056672194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.056672194 + -3.5 x = 11.056672194 + -3.5 Combine like terms: 11.056672194 + -3.5 = 7.556672194 x = 7.556672194 Simplifying x = 7.556672194Subproblem 2
x + 3.5 = -11.056672194 Simplifying x + 3.5 = -11.056672194 Reorder the terms: 3.5 + x = -11.056672194 Solving 3.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.056672194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.056672194 + -3.5 x = -11.056672194 + -3.5 Combine like terms: -11.056672194 + -3.5 = -14.556672194 x = -14.556672194 Simplifying x = -14.556672194Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.556672194, -14.556672194}Solution
x = {7.556672194, -14.556672194}
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