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Simplifying 2x2 + -14x = 38 Reorder the terms: -14x + 2x2 = 38 Solving -14x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + -14x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -7x + x2)' equal to zero and attempt to solve: Simplifying -19 + -7x + x2 = 0 Solving -19 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -7x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -7x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -7x + x2 = 0 + 19 -7x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -7x + x2 = 19 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 = 19 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 19 + 12.25 Combine like terms: 19 + 12.25 = 31.25 12.25 + -7x + x2 = 31.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -3.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -3.5 = 5.590169944 Simplifying x + -3.5 = 5.590169944 Reorder the terms: -3.5 + x = 5.590169944 Solving -3.5 + x = 5.590169944 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 = 5.590169944 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.590169944 + 3.5 x = 5.590169944 + 3.5 Combine like terms: 5.590169944 + 3.5 = 9.090169944 x = 9.090169944 Simplifying x = 9.090169944Subproblem 2
x + -3.5 = -5.590169944 Simplifying x + -3.5 = -5.590169944 Reorder the terms: -3.5 + x = -5.590169944 Solving -3.5 + x = -5.590169944 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 = -5.590169944 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.590169944 + 3.5 x = -5.590169944 + 3.5 Combine like terms: -5.590169944 + 3.5 = -2.090169944 x = -2.090169944 Simplifying x = -2.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.090169944, -2.090169944}Solution
x = {9.090169944, -2.090169944}
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