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Simplifying 2x2 + -2x + -190 = 0 Reorder the terms: -190 + -2x + 2x2 = 0 Solving -190 + -2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + -1x + x2)' equal to zero and attempt to solve: Simplifying -95 + -1x + x2 = 0 Solving -95 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -1x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + -1x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -1x + x2 = 0 + 95 -1x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 -1x + x2 = 95 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 95 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 95 + 0.25 Combine like terms: 95 + 0.25 = 95.25 0.25 + -1x + x2 = 95.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (x + -0.5) equal to 9.759610648 and -9.759610648.Subproblem 1
x + -0.5 = 9.759610648 Simplifying x + -0.5 = 9.759610648 Reorder the terms: -0.5 + x = 9.759610648 Solving -0.5 + x = 9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.759610648 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.759610648 + 0.5 x = 9.759610648 + 0.5 Combine like terms: 9.759610648 + 0.5 = 10.259610648 x = 10.259610648 Simplifying x = 10.259610648Subproblem 2
x + -0.5 = -9.759610648 Simplifying x + -0.5 = -9.759610648 Reorder the terms: -0.5 + x = -9.759610648 Solving -0.5 + x = -9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.759610648 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.759610648 + 0.5 x = -9.759610648 + 0.5 Combine like terms: -9.759610648 + 0.5 = -9.259610648 x = -9.259610648 Simplifying x = -9.259610648Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.259610648, -9.259610648}Solution
x = {10.259610648, -9.259610648}
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