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Simplifying 4x2 + -2x + -380 = 360 Reorder the terms: -380 + -2x + 4x2 = 360 Solving -380 + -2x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -380 + -360 + -2x + 4x2 = 360 + -360 Combine like terms: -380 + -360 = -740 -740 + -2x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -740 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-370 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-370 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -370 + -1x + 2x2 = 0 Solving -370 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -185 + -0.5x + x2 = 0 Move the constant term to the right: Add '185' to each side of the equation. -185 + -0.5x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + -0.5x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + -0.5x + x2 = 0 + 185 -0.5x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 -0.5x + x2 = 185 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 185 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 185 + 0.0625 Combine like terms: 185 + 0.0625 = 185.0625 0.0625 + -0.5x + x2 = 185.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 185.0625 Calculate the square root of the right side: 13.60376786 Break this problem into two subproblems by setting (x + -0.25) equal to 13.60376786 and -13.60376786.Subproblem 1
x + -0.25 = 13.60376786 Simplifying x + -0.25 = 13.60376786 Reorder the terms: -0.25 + x = 13.60376786 Solving -0.25 + x = 13.60376786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 13.60376786 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 13.60376786 + 0.25 x = 13.60376786 + 0.25 Combine like terms: 13.60376786 + 0.25 = 13.85376786 x = 13.85376786 Simplifying x = 13.85376786Subproblem 2
x + -0.25 = -13.60376786 Simplifying x + -0.25 = -13.60376786 Reorder the terms: -0.25 + x = -13.60376786 Solving -0.25 + x = -13.60376786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -13.60376786 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -13.60376786 + 0.25 x = -13.60376786 + 0.25 Combine like terms: -13.60376786 + 0.25 = -13.35376786 x = -13.35376786 Simplifying x = -13.35376786Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.85376786, -13.35376786}Solution
x = {13.85376786, -13.35376786}
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