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Simplifying 5x(68 + -1x) = 530 (68 * 5x + -1x * 5x) = 530 (340x + -5x2) = 530 Solving 340x + -5x2 = 530 Solving for variable 'x'. Reorder the terms: -530 + 340x + -5x2 = 530 + -530 Combine like terms: 530 + -530 = 0 -530 + 340x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-106 + 68x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-106 + 68x + -1x2)' equal to zero and attempt to solve: Simplifying -106 + 68x + -1x2 = 0 Solving -106 + 68x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 106 + -68x + x2 = 0 Move the constant term to the right: Add '-106' to each side of the equation. 106 + -68x + -106 + x2 = 0 + -106 Reorder the terms: 106 + -106 + -68x + x2 = 0 + -106 Combine like terms: 106 + -106 = 0 0 + -68x + x2 = 0 + -106 -68x + x2 = 0 + -106 Combine like terms: 0 + -106 = -106 -68x + x2 = -106 The x term is -68x. Take half its coefficient (-34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. -68x + 1156 + x2 = -106 + 1156 Reorder the terms: 1156 + -68x + x2 = -106 + 1156 Combine like terms: -106 + 1156 = 1050 1156 + -68x + x2 = 1050 Factor a perfect square on the left side: (x + -34)(x + -34) = 1050 Calculate the square root of the right side: 32.403703492 Break this problem into two subproblems by setting (x + -34) equal to 32.403703492 and -32.403703492.Subproblem 1
x + -34 = 32.403703492 Simplifying x + -34 = 32.403703492 Reorder the terms: -34 + x = 32.403703492 Solving -34 + x = 32.403703492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = 32.403703492 + 34 Combine like terms: -34 + 34 = 0 0 + x = 32.403703492 + 34 x = 32.403703492 + 34 Combine like terms: 32.403703492 + 34 = 66.403703492 x = 66.403703492 Simplifying x = 66.403703492Subproblem 2
x + -34 = -32.403703492 Simplifying x + -34 = -32.403703492 Reorder the terms: -34 + x = -32.403703492 Solving -34 + x = -32.403703492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = -32.403703492 + 34 Combine like terms: -34 + 34 = 0 0 + x = -32.403703492 + 34 x = -32.403703492 + 34 Combine like terms: -32.403703492 + 34 = 1.596296508 x = 1.596296508 Simplifying x = 1.596296508Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.403703492, 1.596296508}Solution
x = {66.403703492, 1.596296508}
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