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Simplifying 2x2 + -15x + 117 + x2 + -8x = 180 Reorder the terms: 117 + -15x + -8x + 2x2 + x2 = 180 Combine like terms: -15x + -8x = -23x 117 + -23x + 2x2 + x2 = 180 Combine like terms: 2x2 + x2 = 3x2 117 + -23x + 3x2 = 180 Solving 117 + -23x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 117 + -180 + -23x + 3x2 = 180 + -180 Combine like terms: 117 + -180 = -63 -63 + -23x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -63 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -7.666666667x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -7.666666667x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -7.666666667x + x2 = 0 + 21 -7.666666667x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -7.666666667x + x2 = 21 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 21 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 21 + 14.69444445 Combine like terms: 21 + 14.69444445 = 35.69444445 14.69444445 + -7.666666667x + x2 = 35.69444445 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 35.69444445 Calculate the square root of the right side: 5.974482777 Break this problem into two subproblems by setting (x + -3.833333334) equal to 5.974482777 and -5.974482777.Subproblem 1
x + -3.833333334 = 5.974482777 Simplifying x + -3.833333334 = 5.974482777 Reorder the terms: -3.833333334 + x = 5.974482777 Solving -3.833333334 + x = 5.974482777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 5.974482777 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 5.974482777 + 3.833333334 x = 5.974482777 + 3.833333334 Combine like terms: 5.974482777 + 3.833333334 = 9.807816111 x = 9.807816111 Simplifying x = 9.807816111Subproblem 2
x + -3.833333334 = -5.974482777 Simplifying x + -3.833333334 = -5.974482777 Reorder the terms: -3.833333334 + x = -5.974482777 Solving -3.833333334 + x = -5.974482777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -5.974482777 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -5.974482777 + 3.833333334 x = -5.974482777 + 3.833333334 Combine like terms: -5.974482777 + 3.833333334 = -2.141149443 x = -2.141149443 Simplifying x = -2.141149443Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.807816111, -2.141149443}
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