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Simplifying x(5x + 2) = 2x2 + -14x + 9 Reorder the terms: x(2 + 5x) = 2x2 + -14x + 9 (2 * x + 5x * x) = 2x2 + -14x + 9 (2x + 5x2) = 2x2 + -14x + 9 Reorder the terms: 2x + 5x2 = 9 + -14x + 2x2 Solving 2x + 5x2 = 9 + -14x + 2x2 Solving for variable 'x'. Reorder the terms: -9 + 2x + 14x + 5x2 + -2x2 = 9 + -14x + 2x2 + -9 + 14x + -2x2 Combine like terms: 2x + 14x = 16x -9 + 16x + 5x2 + -2x2 = 9 + -14x + 2x2 + -9 + 14x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -9 + 16x + 3x2 = 9 + -14x + 2x2 + -9 + 14x + -2x2 Reorder the terms: -9 + 16x + 3x2 = 9 + -9 + -14x + 14x + 2x2 + -2x2 Combine like terms: 9 + -9 = 0 -9 + 16x + 3x2 = 0 + -14x + 14x + 2x2 + -2x2 -9 + 16x + 3x2 = -14x + 14x + 2x2 + -2x2 Combine like terms: -14x + 14x = 0 -9 + 16x + 3x2 = 0 + 2x2 + -2x2 -9 + 16x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.333333333x + x2 = 0 + 3 5.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.333333333x + x2 = 3 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 3 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 3 + 7.111111113 Combine like terms: 3 + 7.111111113 = 10.111111113 7.111111113 + 5.333333333x + x2 = 10.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 10.111111113 Calculate the square root of the right side: 3.179797338 Break this problem into two subproblems by setting (x + 2.666666667) equal to 3.179797338 and -3.179797338.Subproblem 1
x + 2.666666667 = 3.179797338 Simplifying x + 2.666666667 = 3.179797338 Reorder the terms: 2.666666667 + x = 3.179797338 Solving 2.666666667 + x = 3.179797338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 3.179797338 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 3.179797338 + -2.666666667 x = 3.179797338 + -2.666666667 Combine like terms: 3.179797338 + -2.666666667 = 0.513130671 x = 0.513130671 Simplifying x = 0.513130671Subproblem 2
x + 2.666666667 = -3.179797338 Simplifying x + 2.666666667 = -3.179797338 Reorder the terms: 2.666666667 + x = -3.179797338 Solving 2.666666667 + x = -3.179797338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -3.179797338 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -3.179797338 + -2.666666667 x = -3.179797338 + -2.666666667 Combine like terms: -3.179797338 + -2.666666667 = -5.846464005 x = -5.846464005 Simplifying x = -5.846464005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.513130671, -5.846464005}
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