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Simplifying 2x2 + 14x + -84 = 0 Reorder the terms: -84 + 14x + 2x2 = 0 Solving -84 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 7x + x2)' equal to zero and attempt to solve: Simplifying -42 + 7x + x2 = 0 Solving -42 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 7x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 7x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 7x + x2 = 0 + 42 7x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 7x + x2 = 42 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 = 42 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 42 + 12.25 Combine like terms: 42 + 12.25 = 54.25 12.25 + 7x + x2 = 54.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 3.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 3.5 = 7.365459931 Simplifying x + 3.5 = 7.365459931 Reorder the terms: 3.5 + x = 7.365459931 Solving 3.5 + x = 7.365459931 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 = 7.365459931 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.365459931 + -3.5 x = 7.365459931 + -3.5 Combine like terms: 7.365459931 + -3.5 = 3.865459931 x = 3.865459931 Simplifying x = 3.865459931Subproblem 2
x + 3.5 = -7.365459931 Simplifying x + 3.5 = -7.365459931 Reorder the terms: 3.5 + x = -7.365459931 Solving 3.5 + x = -7.365459931 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 = -7.365459931 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.365459931 + -3.5 x = -7.365459931 + -3.5 Combine like terms: -7.365459931 + -3.5 = -10.865459931 x = -10.865459931 Simplifying x = -10.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.865459931, -10.865459931}Solution
x = {3.865459931, -10.865459931}
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