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Simplifying 0 = 3x2 + -23x + -98 Reorder the terms: 0 = -98 + -23x + 3x2 Solving 0 = -98 + -23x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 98 = 98 98 + 23x + -3x2 = -98 + -23x + 3x2 + 98 + 23x + -3x2 Reorder the terms: 98 + 23x + -3x2 = -98 + 98 + -23x + 23x + 3x2 + -3x2 Combine like terms: -98 + 98 = 0 98 + 23x + -3x2 = 0 + -23x + 23x + 3x2 + -3x2 98 + 23x + -3x2 = -23x + 23x + 3x2 + -3x2 Combine like terms: -23x + 23x = 0 98 + 23x + -3x2 = 0 + 3x2 + -3x2 98 + 23x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 98 + 23x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -32.66666667 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '32.66666667' to each side of the equation. -32.66666667 + -7.666666667x + 32.66666667 + x2 = 0 + 32.66666667 Reorder the terms: -32.66666667 + 32.66666667 + -7.666666667x + x2 = 0 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + -7.666666667x + x2 = 0 + 32.66666667 -7.666666667x + x2 = 0 + 32.66666667 Combine like terms: 0 + 32.66666667 = 32.66666667 -7.666666667x + x2 = 32.66666667 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 = 32.66666667 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 32.66666667 + 14.69444445 Combine like terms: 32.66666667 + 14.69444445 = 47.36111112 14.69444445 + -7.666666667x + x2 = 47.36111112 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 47.36111112 Calculate the square root of the right side: 6.881940941 Break this problem into two subproblems by setting (x + -3.833333334) equal to 6.881940941 and -6.881940941.Subproblem 1
x + -3.833333334 = 6.881940941 Simplifying x + -3.833333334 = 6.881940941 Reorder the terms: -3.833333334 + x = 6.881940941 Solving -3.833333334 + x = 6.881940941 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 = 6.881940941 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 6.881940941 + 3.833333334 x = 6.881940941 + 3.833333334 Combine like terms: 6.881940941 + 3.833333334 = 10.715274275 x = 10.715274275 Simplifying x = 10.715274275Subproblem 2
x + -3.833333334 = -6.881940941 Simplifying x + -3.833333334 = -6.881940941 Reorder the terms: -3.833333334 + x = -6.881940941 Solving -3.833333334 + x = -6.881940941 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 = -6.881940941 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -6.881940941 + 3.833333334 x = -6.881940941 + 3.833333334 Combine like terms: -6.881940941 + 3.833333334 = -3.048607607 x = -3.048607607 Simplifying x = -3.048607607Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.715274275, -3.048607607}
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