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Simplifying -0.82x2 + 10x + 4 = 18 Reorder the terms: 4 + 10x + -0.82x2 = 18 Solving 4 + 10x + -0.82x2 = 18 Solving for variable 'x'. Reorder the terms: 4 + -18 + 10x + -0.82x2 = 18 + -18 Combine like terms: 4 + -18 = -14 -14 + 10x + -0.82x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -14 + 10x + -0.82x2 = 0 Begin completing the square. Divide all terms by -0.82 the coefficient of the squared term: Divide each side by '-0.82'. 17.07317073 + -12.19512195x + x2 = 0 Move the constant term to the right: Add '-17.07317073' to each side of the equation. 17.07317073 + -12.19512195x + -17.07317073 + x2 = 0 + -17.07317073 Reorder the terms: 17.07317073 + -17.07317073 + -12.19512195x + x2 = 0 + -17.07317073 Combine like terms: 17.07317073 + -17.07317073 = 0.00000000 0.00000000 + -12.19512195x + x2 = 0 + -17.07317073 -12.19512195x + x2 = 0 + -17.07317073 Combine like terms: 0 + -17.07317073 = -17.07317073 -12.19512195x + x2 = -17.07317073 The x term is -12.19512195x. Take half its coefficient (-6.097560975). Square it (37.18024984) and add it to both sides. Add '37.18024984' to each side of the equation. -12.19512195x + 37.18024984 + x2 = -17.07317073 + 37.18024984 Reorder the terms: 37.18024984 + -12.19512195x + x2 = -17.07317073 + 37.18024984 Combine like terms: -17.07317073 + 37.18024984 = 20.10707911 37.18024984 + -12.19512195x + x2 = 20.10707911 Factor a perfect square on the left side: (x + -6.097560975)(x + -6.097560975) = 20.10707911 Calculate the square root of the right side: 4.484091782 Break this problem into two subproblems by setting (x + -6.097560975) equal to 4.484091782 and -4.484091782.Subproblem 1
x + -6.097560975 = 4.484091782 Simplifying x + -6.097560975 = 4.484091782 Reorder the terms: -6.097560975 + x = 4.484091782 Solving -6.097560975 + x = 4.484091782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.097560975' to each side of the equation. -6.097560975 + 6.097560975 + x = 4.484091782 + 6.097560975 Combine like terms: -6.097560975 + 6.097560975 = 0.000000000 0.000000000 + x = 4.484091782 + 6.097560975 x = 4.484091782 + 6.097560975 Combine like terms: 4.484091782 + 6.097560975 = 10.581652757 x = 10.581652757 Simplifying x = 10.581652757Subproblem 2
x + -6.097560975 = -4.484091782 Simplifying x + -6.097560975 = -4.484091782 Reorder the terms: -6.097560975 + x = -4.484091782 Solving -6.097560975 + x = -4.484091782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.097560975' to each side of the equation. -6.097560975 + 6.097560975 + x = -4.484091782 + 6.097560975 Combine like terms: -6.097560975 + 6.097560975 = 0.000000000 0.000000000 + x = -4.484091782 + 6.097560975 x = -4.484091782 + 6.097560975 Combine like terms: -4.484091782 + 6.097560975 = 1.613469193 x = 1.613469193 Simplifying x = 1.613469193Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.581652757, 1.613469193}
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