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Simplifying 2x + 4x(28 + -1x) = 80 2x + (28 * 4x + -1x * 4x) = 80 2x + (112x + -4x2) = 80 Combine like terms: 2x + 112x = 114x 114x + -4x2 = 80 Solving 114x + -4x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 114x + -4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 114x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 57x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 57x + -2x2)' equal to zero and attempt to solve: Simplifying -40 + 57x + -2x2 = 0 Solving -40 + 57x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 20 + -28.5x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -28.5x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -28.5x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -28.5x + x2 = 0 + -20 -28.5x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -28.5x + x2 = -20 The x term is -28.5x. Take half its coefficient (-14.25). Square it (203.0625) and add it to both sides. Add '203.0625' to each side of the equation. -28.5x + 203.0625 + x2 = -20 + 203.0625 Reorder the terms: 203.0625 + -28.5x + x2 = -20 + 203.0625 Combine like terms: -20 + 203.0625 = 183.0625 203.0625 + -28.5x + x2 = 183.0625 Factor a perfect square on the left side: (x + -14.25)(x + -14.25) = 183.0625 Calculate the square root of the right side: 13.530059128 Break this problem into two subproblems by setting (x + -14.25) equal to 13.530059128 and -13.530059128.Subproblem 1
x + -14.25 = 13.530059128 Simplifying x + -14.25 = 13.530059128 Reorder the terms: -14.25 + x = 13.530059128 Solving -14.25 + x = 13.530059128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.25' to each side of the equation. -14.25 + 14.25 + x = 13.530059128 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + x = 13.530059128 + 14.25 x = 13.530059128 + 14.25 Combine like terms: 13.530059128 + 14.25 = 27.780059128 x = 27.780059128 Simplifying x = 27.780059128Subproblem 2
x + -14.25 = -13.530059128 Simplifying x + -14.25 = -13.530059128 Reorder the terms: -14.25 + x = -13.530059128 Solving -14.25 + x = -13.530059128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.25' to each side of the equation. -14.25 + 14.25 + x = -13.530059128 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + x = -13.530059128 + 14.25 x = -13.530059128 + 14.25 Combine like terms: -13.530059128 + 14.25 = 0.719940872 x = 0.719940872 Simplifying x = 0.719940872Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.780059128, 0.719940872}Solution
x = {27.780059128, 0.719940872}
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