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Simplifying 10x2 + -76x + 80 = 0 Reorder the terms: 80 + -76x + 10x2 = 0 Solving 80 + -76x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -38x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -38x + 5x2)' equal to zero and attempt to solve: Simplifying 40 + -38x + 5x2 = 0 Solving 40 + -38x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + -7.6x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7.6x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -7.6x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7.6x + x2 = 0 + -8 -7.6x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7.6x + x2 = -8 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = -8 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = -8 + 14.44 Combine like terms: -8 + 14.44 = 6.44 14.44 + -7.6x + x2 = 6.44 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 6.44 Calculate the square root of the right side: 2.537715508 Break this problem into two subproblems by setting (x + -3.8) equal to 2.537715508 and -2.537715508.Subproblem 1
x + -3.8 = 2.537715508 Simplifying x + -3.8 = 2.537715508 Reorder the terms: -3.8 + x = 2.537715508 Solving -3.8 + x = 2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 2.537715508 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 2.537715508 + 3.8 x = 2.537715508 + 3.8 Combine like terms: 2.537715508 + 3.8 = 6.337715508 x = 6.337715508 Simplifying x = 6.337715508Subproblem 2
x + -3.8 = -2.537715508 Simplifying x + -3.8 = -2.537715508 Reorder the terms: -3.8 + x = -2.537715508 Solving -3.8 + x = -2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -2.537715508 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -2.537715508 + 3.8 x = -2.537715508 + 3.8 Combine like terms: -2.537715508 + 3.8 = 1.262284492 x = 1.262284492 Simplifying x = 1.262284492Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.337715508, 1.262284492}Solution
x = {6.337715508, 1.262284492}
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