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Simplifying 13x2 + -78x = 153 Reorder the terms: -78x + 13x2 = 153 Solving -78x + 13x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + -78x + 13x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + -78x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -11.76923077 + -6x + x2 = 0 Move the constant term to the right: Add '11.76923077' to each side of the equation. -11.76923077 + -6x + 11.76923077 + x2 = 0 + 11.76923077 Reorder the terms: -11.76923077 + 11.76923077 + -6x + x2 = 0 + 11.76923077 Combine like terms: -11.76923077 + 11.76923077 = 0.00000000 0.00000000 + -6x + x2 = 0 + 11.76923077 -6x + x2 = 0 + 11.76923077 Combine like terms: 0 + 11.76923077 = 11.76923077 -6x + x2 = 11.76923077 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 11.76923077 + 9 Reorder the terms: 9 + -6x + x2 = 11.76923077 + 9 Combine like terms: 11.76923077 + 9 = 20.76923077 9 + -6x + x2 = 20.76923077 Factor a perfect square on the left side: (x + -3)(x + -3) = 20.76923077 Calculate the square root of the right side: 4.557327152 Break this problem into two subproblems by setting (x + -3) equal to 4.557327152 and -4.557327152.Subproblem 1
x + -3 = 4.557327152 Simplifying x + -3 = 4.557327152 Reorder the terms: -3 + x = 4.557327152 Solving -3 + x = 4.557327152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.557327152 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.557327152 + 3 x = 4.557327152 + 3 Combine like terms: 4.557327152 + 3 = 7.557327152 x = 7.557327152 Simplifying x = 7.557327152Subproblem 2
x + -3 = -4.557327152 Simplifying x + -3 = -4.557327152 Reorder the terms: -3 + x = -4.557327152 Solving -3 + x = -4.557327152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.557327152 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.557327152 + 3 x = -4.557327152 + 3 Combine like terms: -4.557327152 + 3 = -1.557327152 x = -1.557327152 Simplifying x = -1.557327152Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.557327152, -1.557327152}
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