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Simplifying 3x2 + -69x + 5 = 0 Reorder the terms: 5 + -69x + 3x2 = 0 Solving 5 + -69x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -23x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -23x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -23x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -23x + x2 = 0 + -1.666666667 -23x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -23x + x2 = -1.666666667 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -1.666666667 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -1.666666667 + 132.25 Combine like terms: -1.666666667 + 132.25 = 130.583333333 132.25 + -23x + x2 = 130.583333333 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 130.583333333 Calculate the square root of the right side: 11.427306478 Break this problem into two subproblems by setting (x + -11.5) equal to 11.427306478 and -11.427306478.Subproblem 1
x + -11.5 = 11.427306478 Simplifying x + -11.5 = 11.427306478 Reorder the terms: -11.5 + x = 11.427306478 Solving -11.5 + x = 11.427306478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.427306478 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.427306478 + 11.5 x = 11.427306478 + 11.5 Combine like terms: 11.427306478 + 11.5 = 22.927306478 x = 22.927306478 Simplifying x = 22.927306478Subproblem 2
x + -11.5 = -11.427306478 Simplifying x + -11.5 = -11.427306478 Reorder the terms: -11.5 + x = -11.427306478 Solving -11.5 + x = -11.427306478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.427306478 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.427306478 + 11.5 x = -11.427306478 + 11.5 Combine like terms: -11.427306478 + 11.5 = 0.072693522 x = 0.072693522 Simplifying x = 0.072693522Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.927306478, 0.072693522}
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